strange moves in nimzoindian how to respond
With 3 .a3 it seems he wants to play the Petrosian System against the Queen's Indian which would happen after 3...b6 4. Nf3 Bb7. What I usually do however is play 3...c5 here and see what he does about his d pawn. If he plays 4. d5 then I head for a Benoni but transpositions are also possible into English or Sicilian after 3...c5.

Before deciding on a spot for your dark-squared Bishop, you should decide what sort of central formation you want. That will influence your choice of squares for the dsB.
If you are going to play into a Queen's Indian, or a Queen's Gambit Declined Orthodox formation (Pawns on f7-e6-d5) then the Bishop will belong on e7. If you are heading for a Tarrasch Defense formation (QGD Orthodox with an early c5) then the Bishop will end up either on e7 or d6, depending. If you are heading for a Benoni formation (c5 to provoke White's d4-d5 push) then the Bishop will likely fianchetto to g7 instead.
In any case, you should be hoping to play a line where White's a3 move is not particularly relevant, so that he pays a price in opportunity cost in return for preventing your Nimzo.

Both tarrasch and benoni are dodgy...
Orthodox or Semi Slav is a better bet.
At our level all openings are dodgy.

lol...
By dodgy, i meaning that... tarrasch can lead to an iqp and benoni is very difficult to play.

Chess is not a game of cooperation. You will always play people who read the whole "anti-matter".
So ...d5 & ...c5 are ok but rather no QID or Bogo. I would play a Benoni with White's a move down. The KID might be an idea cause White made a nullmove, so with a later c5 or e6-e5 Black could be on track.

You can play 3. ... c5 as was already proposed. When White then transposes in a Benoni with d5 then a3 is no useful move. Usually in the Benoni White plays a4 in one go to prevent b5.
But most White players who play 3. a3 (avoiding the Nimzoindian and the Bogo-Indian) don‘t want the Benoni either (that‘s my experience). They play 4. Nf3.
If you don‘t like that you have the other option of playing 3. ... d5, going for a Queen‘s Gambit. There 3.a3 isn‘t helpful either.

You can play 3. ... c5 as was already proposed. When White then transposes in a Benoni with d5 then a3 is no useful move. Usually in the Benoni White plays a4 in one go to prevent b5.
But most White players who play 3. a3 (avoiding the Nimzoindian and the Bogo-Indian) don‘t want the Benoni either (that‘s my experience). They play 4. Nf3.
If you don‘t like that you have the other option of playing 3. ... d5, going for a Queen‘s Gambit. There 3.a3 isn‘t helpful either.
Watch out... a3!?
https://www.chessbomb.com/arena/2018-bundesliga/11-Korobov_Anton-Anand_Viswanathan

Yes I encounter 3.a3 only once. You can t play the Nimzo-Indian after this rare third move.
But black has two good moves here. 3....c5 and you get a Benoni with a3.
Normaly in a Benoni white plays a4. Thus this is a kind of lost of a tempo.
Thus this is playable for black. Some white players like the Benoni so much that they even want to play it with a tempo down. The other possibiloty is 3....d5 also a good move and black gets a Queens gambit declined also with a a3 move for white that is not the most promising move. So no worries for Black after 3.a3.

The discussion here concerns 1.d4 Nf6 2. c4 e6 3. a3.
I claimed that 3. a3 isn‘t very useful when going in Benoni or QGD. That doesn‘t mean a3 is never useful. It sure can be very useful. Korobov played in the 6th move.

You can play 3. ... c5 as was already proposed. When White then transposes in a Benoni with d5 then a3 is no useful move. Usually in the Benoni White plays a4 in one go to prevent b5.
But most White players who play 3. a3 (avoiding the Nimzoindian and the Bogo-Indian) don‘t want the Benoni either (that‘s my experience). They play 4. Nf3.
If you don‘t like that you have the other option of playing 3. ... d5, going for a Queen‘s Gambit. There 3.a3 isn‘t helpful either.
Watch out... a3!?
https://www.chessbomb.com/arena/2018-bundesliga/11-Korobov_Anton-Anand_Viswanathan
Here a3 is played much later in a Queens gambit declined. Personly I would also have taken on move 9 with the Bishop and back has no problems.

Uhm, it‘s QGD with an early a3? It‘s a bit later (move 6) but proved useful yet. Where‘s the difference in usefulness?

Any of these choices are decently playable for all of us( cos we dont need serious accuracy for world championship level).
1. One million node analysis of leela ( 3 mins on decent GPU)
2. 1 billion node analysis of Stockfish 10( 3 mins)
3. Database of ICCF players
4. Database of computer opening book( perfect chess, brainfish)
5. Database of OTB human master games.
wow lots of anwers here. i have always played the queens gambit declined but decided it was time for some variation. when i got 3.a3 i just played d5 into a queens gambit style game and its ok i guess but the point was to NOT play a queens gambit. i got to try out stuff and see what i like i will write again after this
Any of these choices are decently playable for all of us( cos we dont need serious accuracy for world championship level).
1. One million node analysis of leela ( 3 mins on decent GPU)
2. 1 billion node analysis of Stockfish 10( 3 mins)
3. Database of ICCF players
4. Database of computer opening book( perfect chess, brainfish)
5. Database of OTB human master games.
I thought you'd be one of the least people advocating a 3 min analysis by an engine.

Any of these choices are decently playable for all of us( cos we dont need serious accuracy for world championship level).
1. One million node analysis of leela ( 3 mins on decent GPU)
2. 1 billion node analysis of Stockfish 10( 3 mins)
3. Database of ICCF players
4. Database of computer opening book( perfect chess, brainfish)
5. Database of OTB human master games.
I thought you'd be one of the least people advocating a 3 min analysis by an engine.
3 min analysis is not the best way to prepare against WCC level, but it is the easiest way to find out how a 3500 rated top player will play in that particular position. (easiest way to see the reason behind choosing a move by looking at the end of principal variation)

In fact, 3 mins analysis of opening with SF is probably the worst among 5 methods I mentioned.
Why?
Because in TCEC SF vs Leela in 100 games match with opening book , SF won marginally 50.5-49.5.
SF without opening book lose horribly to Leela. 44-56.
But it is just punishment among 3500 players with slight inaccuracy, but no human can punish SF's inaccuracy. ( SF line is completely fine for live chess)