for the pull-up bar in my house, I used a bathroom rail for handicap-accessible stalls. No welding needed, and it's sturdy enough to hold several hundred pounds.
>Thats a graet idea...i never thought about that. About how much would one of those cost and where would you buy it?
Home Depot, Lowes, scrap yard, handicap neighbor when he isn't home.
UnImproving Structural Integrity
The strong ties, in this situation, are completely unnecessary. Those are for "real" floor joists, long ones, and will help to prevent your house from being ripped apart by tornado/hurricane/etc.
For 1', 2', 3' spans between 2x4's, just drive two 3 1/2" wood screws ("Deck Screws", but not galvanised unless your loft is subject to rain) from the outside through to the short spans, like you've done on the ends. Might want to consider lag bolts or carriage bolts on the diagonal supports though. Your plywood decking (with 2" wood screws all over) will also firm everything up. Save the bucks though, don't use strong ties unless you're building a 10x10 loft or something. Then you'd better get some 2x6's!
Improving Structural Integrity
The single biggest problem that I see from a structural standpoint is that the 2x4s are merely attached to the 4x4s. Should a large load be applied to the platform, all that is holding the 2x4s up is the skinny cross-section of metal offered by the screws. Using 3/8" or 1/2" carriage bolts instead of screws for these critical connections would be a minor modification to your plans that would make a big difference integrity-wise.
Ideally, the 2x4s should rest directly on top of the 4x4s. Notch the 4x4s to create a shoulder to receive the 2x4s or use a suitable Simpson-type tie to hold the 2x4s in place on their perches atop the 4x4s.
For areas where bracing is needed but headroom is desired, consider using knee braces which don't fill the entire bay. A brace fastened (ideally bolted) a foot or so down from the top of the 4x4 and running up at a 45 degree angle to the 2x4 will stiffen the frame and reduce wobble.
If you're not entirely trusting of the floor that the 4x4s are resting on, place a long 2x4 under several of them. This will distribute the relatively concentrated load that each of them places on the floor over a larger area. If you are dealing with a wood-framed building and have a sense of which way the joists are aligned, set the 2x4 on the floor in such a way that it crosses as many joists as possible.
Lastly, you list 1/4" plywood as the platform material. This is too thin. However, in the photos, it looks like you used something more on the order of 1/2" or 3/4" plywood, a much more appropriate thickness. The 3/4" would be the way to go for larger lofts.
Knock Down Fittings
After looking at your site and some others I did some research into knock down fittings. I thought this information might be useful to others building a loft bed and so I posted it. Hope that's ok. --Robin