From an RSX or Integra, the offset is most likely +45. If the bolt pattern is 5x114 and has a centerbore larger than the MR2's, I don't see why they wouldn't fit. They will be very tucked (and quite ugly in my opinion), but they will fit. I'm pretty sure they will, because I remember seeing a few MR2's with RSX wheels on the MR2 board. But again, they look very tucked.
As for the tires, a 205/55/16 "should" fit on the rear, but I don't think it will fit in the front. A little too tall. A 205/50/16 might fit, but I'd probably go with a 45 to be sure.
Good luck!