What are the sturdiest types of joints for my lofted queen bed frame?
The design you have looks quite solid.  If you really wanted to add a touch more, you could mortise and tenon the joints. That would give it a nice look and add a lot of strength (meaning that you wouldn't see fasteners).  I would certainly glue the joints as well.  I like the notched 2x4 boards.  Keeps you from using metal hardware or trying to toe-nail them in.  

If you can fasten this to the walls of your room, that would add a significant amount of strength to the structure.  Obviously, make sure to fasten it to the studs in the wall and not just drywall.