Olds 307 to Chevy 350 swap in a cutlass?

Yes, although you will need parts.

You will need to check your transmission bell-housing to see if it is a mulitbolt, otherwise it will also needs to be swapped.

You will also need to buy motor mounts for the Chevy Block. The motor mount bolts on the frame have to be removed through the lower control arm holes, (and the control arms must be removed for access).

Your fuel lines wont be on the same side of the frame, so you will need to extend them.

The wiring harness will have the necessary wires to wire the engine, although you will have to extend them, and you will have a big hand full when done.

Your exhaust will also be different.

It can be done in about 2 days, if you have motivated knowledgeable help.