Well, I've beat the game once and I started New Game + on GOG, but I thought it would be cool to have this game on Steam too. On some forums I read that it's possible with some games, but would it work with Oxenfree too? And how can I do that if it's possible?

Hi, I might be too late to this but I had a similar problem, only I wanted to go from Steam to GOG.

The saves are stored in %USERPROFILE%\AppData\LocalLow\Night School Studio\Oxenfree\save\,
and the have a different format between Steam and GOG.

For GOG the file is simply named oxenfree_default.nts, but Steam adds an identifier (I think it's the profile ID encoded as steamID64, go to steamidfinder com) to the file, so it would look like this:
oxenfree_default_123456.nts

Hope that helps anybody with the same problem. :)