Withdraw Draw Offer?

If you offer a draw, in a daily game, and then while waiting for your opponent's move, you go ahead and make a move, can they still accept the draw?

Yes. Draw offers stand until your opponent makes a move or declines/accepts the offer 

I know about draw offers for online chess, but what about OTB? I had many cases where my I offer a draw, and my opponent says, "Wait, let's play out the position", or "wait, let me think while playing a few moves first." Is the draw offer still valid even if they already played many moves after the draw offer, but they never accepted or declined the draw offer? I always feel forced to accept the draw offer even when my opponent's response is annoying, and I don't have enough information on whether I am able to take back the draw offer in those situations. Just to confirm, you can't take back a draw offer even if they hadn't made a move, right? These questions are for OTB Chess specifically.

In OTB you can offer a draw AFTER playing your move and BEFORE pressing the clock, and it is valid until your opponent either accepts it, or declines it (by moving a piece). This is not strictly mandatory, but if you offer a draw under other conditions the arbiter may consider this being a distraction attempt.

So, there is nothing to "take back": If the offer is not accepted before the opponent moves, then it becomes a thing from the past.

Ok thanks, but you didn't really answer my question. I already know how to offer a draw and when to offer it, but I just don't know the weird situations, which I already explained in my first question.

The draw offer stands until declined, verbally or by moving, or accepted. If the other player wants to play on, then that is declining the draw and a new offer would have to be made later but the player couldn't just say after moving that they accept the previous draw offer.