Usually, the university will provide a moving allowance, and have a list of suggested moving companies. Pro movers will haul your stuff in a semi, along with 2-8 other households worth of stuff, route optimized to minimize fuel waste. It's not car-free, but if you need to move a bed, futon, or other similarly sized piece of furniture, it is about as cost and fuel efficient as it gets. Most of us really do want something to sleep on. The less stuff you have, the more other people they can fit in.

If you're doing Japanese style sleeping mat, and do not own many books, a stereo system, a computer printer, a desktop computer, tables, or any musical instruments, odds are you could make the move via Extracycle or bike trailer. Even a really minimalist American usually owns one item that makes that unreasonable :-/.

Doing things purely by human power works best when distances are shorter, or the time frame is fairly long.