M.D.
Have you been excercising throughout your pregnancy? If not, definitely check with your OB or midwife before starting a new regimen. Aside from that disclaimer... :)
Yoga is great - but be careful starting out at 31 weeks. Your joints are much more elastic now in preparation for birth, and you don't want to damage them by over-stretching. Walking is also excellent exercise for the end of pregnancy. Also, I have an exercize ball that I lived on at the end of my pregnancy. I didn't do any of the crazy exercises for non-preggos, but even just sitting on the ball while watching TV or reading is a good workout for your core muscles. It can also help baby get into position.
As for foods - lots and lots of fiber. Fruits, veggies, meat if you eat it, etc. The farther along I got the easier I filled up just because DS took up more room.