They're not really cards, just moderately thick cardboard.
Dimensions are 112mm (l) by 84mm (w)about 1mm deep for the character cards
Dimensions are 81mm (l) by 84mm (w)about 1mm deep for the minion cards
Thanks for the quick response. I'll see if I can find some sleeves that will fit them
Edit: Found sleeves that should work!
It looks like 80x120mm sleeves should work for the minion cards, with trimming for the excess length. For the character cards, Mayday makes an 87x112mm sleeve that should fit them nicely. I've added it to the list with these sleeves. Thanks much for the information.
I realized that I don't actually know how many cards there are. Would you mind telling me how many there are of each size?