What are the main options for fastening MDF to MDF?
It sounds like you are trying to build something in one place, pack it up and re-build it in another.  If this is the case then screws are the way to go for dry fit, and then glue and screws for the final instal. I generally use Course thread dry-wall screws - because I feel they bite and pull MDF the best. 

The only thing here is that there is a limited number of times that you can use the same holes with MDF, the Fiber-board looses a little meterial every time you screw into and out of it. So if you are building in a shop and then transporting onto site and reassembling once you are fine, if you are going to build and then rebuild this many times it will get less stable each time you do it.  

As a side note, I also like to use pocket-hole jointery a lot because I like that it hides the screws from view.  

Also, whenever I build boxes to be re-built I always make sure that I have some small square blocks with me.  I use these blocks to make sure the inside of the box is square, just screw them in and it helps to keep the box from racking side to side.