Am I allowed to store gifts I win in my steam inventory?

You should activate your wins, did you already own the game or whats the point in storing it in your inventory?
Edit: I checked your steam profile, is it the Deadnaut game? Because you have that in your games list & you recently won it, you should tell the one who made the giveaway to make a reroll, if that's the case.

You have to activate your wins.

must be activated our you will get a temp ban

if you win, you MUST activate it!

Nope. you need to activate the game immediately into your steam library. If you don't, you risk a suspension for a game won, received, and not in your library

May I ask, why would you want to store them and not activate?

You must not have read them closely enough then. They state that you must activate all wins on your own account, therefore the answer is no.

no

you cant have read the rules, because then you should know that you have to activate it.

I'd be inclined to say yes, but only for up to a maximum of seven days after receipt, assuming the giveaway is for a gift copy, not a key. Though, many would expect that you would proceed to activate the gift straight away upon receipt.

Reason being is because until that game is activated on your account, you haven't technically received it.
Re-gifting is against the rules, as covered in the FAQ, and there would be little to actually prevent someone receiving a gift copy, waiting 30 days so they can gift it away again, then creating a giveaway for the game themselves just because at some point they decided they didn't want the game after all, despite still receiving it from someone else.

If you are just going to keep them to offer them love in your inventory, then it's okay.
But if you're going to regift them, then No.

Just activate them...

Thank you everyone for your responses. I will add it to my library now.

Simple answer: NOPE!