How to repair a beam of structured 2x10s
The beam should be substantial enough. It's a bit baffling how poorly it was built, though. Were it my house, I'd jack up the beam and fasten it together properly. By doing so you should restore the straightness and rigidity that was originally intended. 


Acquire a length of steel or wooden beam that's long enough to span from one post to the other and substantial enough to carry the load of the beam above. I assume that you have spot footings at the posts, but not between. Jacking between will probably crack your slab. 
Place wooden blocks near each post, and span the temporary beam from one to the other. Run it diagonally from one side to the other so it falls below the upper beam where you need to place the jack. 
Place a 10-ton or better bottle jack on the temporary beam below an intermediate member joint. Use a steel post or 6x6 wooden post with a pad block on top, centered right under the joint. 
Using nails set into the underside of the original beam at each end, install a dryline (carpenter's string) some distance down (say 1"). 
With one or more helpers watching what's happening upstairs, slowly begin jacking the beam into position about 1/4" above the 1" target (string measurement 1-1/4"). This will allow some settling when you remove the jack. Ideally the beam members will slide back into position as you do so. 
Drill for pairs of 1/2" carriage or hex bolts through the entire beam every 12 or 16", 2" from the top and bottom of the beam. Install the bolts with washers and nuts. Tighten well. 
Begin to lower the jack, watching for excessive movement. If things really settle, leave a temporary post at that location while you do the others. 
Move the jack and repeat for each location. 


Notes: 


Watch everything carefully as you work. There's potential here for damage to drywall/plaster, misalignment of doors, binding of plumbing, etc. Proceed slowly and inspect the effects of the movement regularly.
Be sure that you're happy with the results before drilling and installing the bolts. You don't want to have to repeat that work if you decide things won't work in the new  position.
It wouldn't hurt to have an experienced builder have a look at things before you begin. Maybe there's more going on than what you've noticed, and making this fix could be the wrong approach.