The required lots size depends on whether you are dividing a new lot or building on an existing lot. Susan is correct that you need to meet minimum requirements to create a new lot .
You can however build on a smaller lot if it was legal when it was created and you can meet minimum setback requirements. A lot that is 50 feet wide is still very buildable. Even with some caution a lot that is less than 50 feet wide may be buildable.
Do your homework before you buy the lot. Ask your Realtor and more important ask at City Hall. Go to the Zoning and Building Inspector offices and any other offices they suggest. Ask them if they know of ANY reason you would not be able to build on the lot and how you can solve the issue. If it can't be solved pick a different lot.
Existing lots in Oshkosh are limited but there are some that still exist and if you can find one they can be a good choice for your needs.
It is great that youths are getting involved in helping other. Good luck to you... more