What STIs are "testable" and who is infected, anyway?

I recently became sexually active at 21, and my partner is a bit older and has had multiple partners. At this point, we are exclusive, and have used a condom on the few occasions we have had intercourse. I went to the local Planned Parenthood recently, and am now on a birth control pill (I am absolutely sure I don't want or need to be pregnant at this point or ever in my life, personal choice...). I realize that although the pills are great for preventing conception, they are not effective at preventing STI's, where as the condom has at least pretty good effectiveness for many of them.