I got free access to Autodesk software through a student program that I'm doing. And I was wondering if I'm allowed to use the software for other projects after I finish. I want to make some games and publish them on Steam and some other online digital distribution download places (like Android Market, Apple App Store, etc). I want to use 3DS Max to make my game's models, but I'm not sure if that's allowed. Does anyone know?

Most likely, no. You would have to read the EULA for the student version to be sure, but all student editions of software I've seen (Visual Studio and other Microsoft products, Photoshop) are for educational purposes and cannot be used for commercial applications.

Edit:

*Free Autodesk software is for personal use for education purposes and is subject to the terms and conditions of the end-user license and services agreement that accompanies download of the software. The software is for personal use for education purposes and is not intended for classroom or lab use.
[/quote]

Source

You could try and convince them that "learning about how game publishing on Steam works" is educational

Your access is granted by the school and the limitations that apply to the school also apply to your use. You will need to purchase a commercial license for AD tools to distribute assets created with those tools games on Steam, iOS and Android.

So I guess I should just stick with Blender then.