We built our outhouse for $35. We bought planks from a neighbor that use to be on an old house. Try looking for used wood people have to give away or sell cheap. We also drove around and found an old barn someone let us tear down for free.
Aside from that, you should be able to build a small shed for less than a hundred bucks. Try sawmills as opposed to Lowe's and such. Wood is much cheaper there and you can get good second pieces they have a hard time selling. There is also the possibility of cord wood if you have a chainsaw and the time to do it that way.
Have you thought about checking out the sawmills?????? They have rough cut scrap boards that can be bought for cheep. You will need a planer and jointer to finish off the boards, but they will pay for themselves.