How do I tell if my 340 is internally balanced?

I don't have much into it, and came with a brand new set of heads. I could sell the block for more than I paid. I already have a 318 in the car and it runs and drives. I may just take some time and rebuild it.

Yes, find a good, reputable engine shop & go through everything. Hopefully it just needs a proper balancing and the rest is ok. But only then you'll know if the crank needs the correct balancer & converter weights or mallory metal. Also if the pistons & rods can be weight-matched better than factory tolerances. Considering the questions with the block, it might be worth haing the heads checked out too.