I'm planning on making let's play videos of The Sims 2 and The Sims Stories soon, but I'm worried about YouTube giving me copyright strikes for the in-game music. I'm going to mute all the music that's credited to real world artists, but is that good enough? Am I allowed to include the game's purely original music and songs that don't seem to have credits, or is that too risky? How can I find out who owns the copyright for certain songs and go about asking for permission to use them?

They shouldn't strike you for the game's original music.

I think I read that a game's publisher or developer usually doesn't own the copyright for the in-game music. It's owned by the individual artists or by third-party groups or record labels, so even if EA is okay with let's play videos of their games, the music would be outside their jurisdiction. Is this correct, or am I just worrying over nothing?