My bike recently got into a crash (I was not on it) and both wheels were taco'd. Is it safe to take the tires off and use them on a different wheel? What could go wrong and what should I look out for?
It should be perfectly safe to re-use the tyres. Many tyres are stored folded/twisted in their packaging to save space.
I would however recommend carefully inspecting each tyre first, checking for damage to the tread area, sidewalls and tyre bead.
Tyres are flexible in all directions so tacoing the wheel won't in and of itself damage the tyre. However, in real life, it's hard to taco a wheel in an accident without pushing the bike sideways across the road, which may damage the tyres in a similar way to how a hard skid would. You should check the tyres carefully for that sort of damage.
You don't mention the frame at all, so it's not clear whether you're thinking "It's obviously trashed, so I've already disposed of it" or "Hey, it looks fine so I'll keep using it." In case it's the latter, you should inspect it very carefully. A crash that has tacoed both wheels is pretty likely to have bent the frame and potentially damaged the forks. If your plan is to replace the wheels and keep riding the bike, I'd strongly recommend that you get it checked over by a bike shop first.