Android - Is there a way to easily record a phone conversation in-progress?

There are a couple of apps to try. I use Ultimate Voice Recorder which costs $4.99 but works beautifully. You can start recording in the middle of a call.

A quick search on AppBrain brought up Record My Call which is free. I haven't used Record My Call so I can't comment on whether or not it can start in the middle of a call.

Update: Ultimate Voice Recorder does record both sides of the conversation.

Tasker can do this for you no problems. In fact, it's listed on the home page as a particular use case:

make automatic recordings of what you say during phone calls to SD card

Yes, it is possible to record phone calls using Google Voice (but only calls that you receive).