Please post a diagram that display how the werewolf moves.
Werewolf Chess
That would look something like this:
Not all aspects can be made obvious in a static drawing, however. The squares marked in yellow are reached by sliding moves, like a Queen. Those marked in orange can also be reached by direct jumps, e.g. over the white Pawn or black Rook. What is hard to indicate is that when the Werewolf does jump over the Rook to b5, the Rook can be taken en passant. (But this is optional, and white can leave the Rook on c5 if that seems better.) This can be done even if b5 also contained an enemy piece (double capture).

I think you've made the werewolf too powerful. Given it's jumping and double-capture ability plus being unkillable, isn't the werewolf just going to kill everything and leave you with a drawn endgame?
Note that 'unkillable' here only means it will not be eliminated from the game. It will change sides when it is captured, however. So an unprotected Werewolf is even more vulnerable than a Queen: if someone captures your hanging Queen, you 'just' lose a Queen. If someone captures your hanging Werewolf, you not only lose the Werewolf, but the opponent's piece promotes to one! So I am not sure how much this form of unkillability is worth. It is true that it allows you to use the piece more aggressively, when you keep it protected, so it must be worth something.
As to its intrinsic power: the ability to jump to the second square turns out to be almost exactly worth as much on a Queen as all the moves with range > 3 together. So the Werewolf is indeed stronger than Queen, but only bcause of the extra ability to capture the piece it jumps over as a side dish. Although I have not exactly measured how much this is worth, it seems like a manageable increase, because there is only one square you can end on, and the opponent could protect his piece against such a capture by covering that square.
It is in particular choice in how to move on after having made a capture that makes such en-passant captures very dangerous. E.g. the Chu Shogi Lion can capture a neighbor, and then move on as a King, picking any safe square out of 8, including the square where it came from (which usually was safe). This makes it practically impossible to defend against such captures. This is why the Lion is considered worth 1.5x as much as a Queen, even on the Chu 12x12 board (which benefits the Queen). On 8x8 it might be worth about 16 (when Q=9), while a piece that can make the same moves, but without the en-passant ability is worth only ~10.5. So the en-passant captures are worth more than 5 in that case. With only a single destination square per capture, in stead of eight, it seems reasonable that this drops to 1-2.
So yes, the Werwolf is somewhat stronger than Queen, but I think it stays within the bounds of reasonability.

Sorry, I misunderstood the first time, I was thinking that being captured by a king made the werewolf switch sides and nothing else could capture it.

Can the werewolf jump over a piece on the first square without capturing it?
Can it jump over both the occupied first and second square without capturing what was there?
Can it triple-capture?

Can the werewolf jump over a piece on the first square without capturing it?
Can it jump over both the occupied first and second square without capturing what was there?
Can it triple-capture?
I just had to check the meaning of leap in my dictionary.
Can the werewolf jump over a piece on the first square without capturing it?
Can it jump over both the occupied first and second square without capturing what was there?
Can it triple-capture?
1) Yes
2) No, it cannot jump to the second square at all. It can only slide there, meaning that 1st and 2nd square have to be empty to reach it. As indicated in the move diagram, where the Pawn, Rook and Bishop block access to the 3rd square.
3) No
You probably noticed that the Werewolf is inspired by the 'Lion Dog' of (Maka) Dai Dai Shogi. But a piece with triple Lion power, even if only linear, is just too dangerous on 8x8. I thought even allowing 'igui' om the first square would make it too strong. In fact I wonder if historically the Lion Dog would not have been more like this Werewolf, its Lion power only extending to the first 2 squares (i.e. Horned Falcon/Soaring Eagle moves), while the access to the 3rd square was a slide. Like we assume now for the Furious Fiend in those variants. In fact one of the historic manuscripts mentions Furious Fiend = Lion + Lion Dog.
Great, I will watch the game. But don't forget to mention that a King is immune to promotion. Or it would not be clear what happens after K x W. (Immediate loss? Royal Werewolf?)

How do werewolf and joker interact? If a white Knight takes a black werewolf then what can a black joker do? Move like a knight or like a werewolf?

The reason why I ask is that I have just finished a game with Werewolf and Joker.
https://www.chess.com/forum/view/chess960-chess-variants/bulldog-chess-evert823-junebug444-lots-of-pieces
It has been said that if white promotes a pawn to Queen, the black Joker is allowed to move like a Queen. If I remember well even by Henk van Haeringen himself. So then the same question rises when a piece becomes a Werewolf and there is a Joker on the board.

I just had this thought: when we introduce a piece and - as piece inventor - we add rules that prevent that our piece disappears too easily by trade, there is a very simple rule we could add: allow that particular piece to be kept in hand and dropped.
Not all pieces, like in Shogi, but only that precious piece. Sounds like a very good alternative for the Lion trade rules in Chu.
I have not visited this thread for a long time.
As to the Joker: it depends on how the Joker is defined. In Superchess it apparently mimics the piece at the end of the turn, rather than at the start. But the Werewolf is not in Superchess.
The re-dropping rule you propose needs some refinement. You would not want the opponent to drop the 'protected' piece back when it was captured by, or traded for a piece of a diferent type. That would make it practically an 'iron' piece.
I you mean Shogi/Crazyhouse-style redropping (i.e. after color flip), it would make the piece very vulnerable, especially if it is a strong one: it would no longer be acceptable to trade it even for two other pieces. E.g. Q or 2R would not be a good deal if the opponent gets a Q in hand by that.
In addition, I also would not consider it a good thing if a piece could never disappear. This is why I made the King immune to Werewolf contageon. And in Chu Shogi Lions do not always survive to the very end.
I conceived a new Chess variant that should be easy to play for orthodox Chess players using a normal Chess set. It is played by all the standard FIDE rules, with the following exceptions:
The Queen in the initial setup is replaced by a Werewolf. The latter moves as a Queen, but over a maximum distance of 3 squares only (i.e. from d1 you could play Wd4, if the intervening squares are empty, but never Wd5). But it can also directly leap to the second square, if it wants to end there (i.e. you can play Wd1-d3 even when d2 is still present). If it makes such a leap, it can optionally capture the enemy piece it leaps over, (in the Checkers way, as it were), possibly in addition to what it captures on the destination square in the normal way.
A Werewolf is thus capable of double capture! This makes it stronger than an ordinary Queen. (The non-capturing leap to the second square already compensates for the missing distant moves.) It can also capture protected pieces with impunity, by jumping over them to a safe square on their other side.
Now this game would not be very interesting if the Werewolfs could be quickly traded, leaving you with a boring normal Chess end-game. Fortunately this cannot happen, because Werewolfs are almost immortal! Only Kings can kill them, as only these can afford the silver weaponry needed to do the job. But when a non-royal piece captures a Werewolf, it becomes one. (Technically: the attack is suicide, but 'turns' the Werewolf, which fights on your side after it.) As Kings normally don't participate in middle-game tactics, this guarantees survival of at least one Werewolf until the end-game. (One can disappear from the game when Werewolfs capture each other.)
Pawns promote to Rook, Bishop or Knight, when they reach last rank. They cannot promote to Queen or Werewolf. (They do shapeshift into a Werewolf when capturing a Werewolf on the last rank, though.)
Tactical ramifications
Even putting their dangerous leap-capture aside, the fact that Werewolfs are practically unkillable already makes them much more dangerous than an ordinary Queen. Because as long as you keep them sufficiently protected, any tactical exchange on the square where they stand will leave you with a Werewolf there. E.g. attacking a Werewolf protected by a Pawn becomes the same as attacking a Pawn protected by a Werewolf. (E.g. if you capture it with a Knight, the Knight becomes your Werewolf, but then he recaptures with the Pawn, which now becomes his Werewolf, and you lost Knight for Pawn. And his Werewolf would still be exactly where it was before!) So Werewolfs can boldly go in front of their troops, exerting there dangerous moves from close by.
Equipment
You can use Queens to represent the Werewolfs. This might not even be very confusing, as they move approximately the same. But in that case you would need spare Queens, as sometimes both Werewolfs are on the same side, even if only transiently during tactics. You could also use a stack of Draughts chips of different colors, (also fitting, because the Werewolf can capture as a Checker), the top color determining which side the Werewolf is on. When a piece captures the Werewolf you can then simply discard that piece, and flip the stack to put your own color on top.