I was asked to teach a robotics class and found several RCX bricks in storage. Can I use these bricks with the Mindstorms NXT 2.0 software? If not, what would be the software I would need to use the RCX bricks?
No, the standard NXT-G software provided by LEGO will not allow you to program a RCX brick.
Outside of official software, your best bet is probably to use NQC which is C-like; there's also NXC for the NXT which is similar.
There are a lot of others which have been discussed in the following questions: Is there any other way to program the Lego Mindstorms NXT other than the provided software? and Can I write programs for the LEGO RCX 2.0 in Java/C++?.