Mac Pro 2007 crashes repeatedly
That could be a lot of things. It could be the system, it could be the hard drive, it could be a drive cable...it could be lots of things. It sounds like it's a drive problem.

The following links are "how-to" links from the guys that make Scannerz. One is how to use activity monitor to try and isolate processes that are using too much CPU/Memory etc and the other is about bad hard drives. The Activity Monitor post says it's about Mountain Lion, and clearly some of the topics are Mountain Lion specific, but in general it shows how to use Activity Monitor and some tricks I never new about. Here are the links:

http://www.scsc-online.com/Activity%20Monitor.html

http://www.scsc-online.com/Bad%20Hard%20Drive%20Signs%20and%20Symptoms.html

Although you have an SSD, I was surprised to see a post on MacRumors where someone used Scannerz on a system that was having problems that sounded similar to yours. Scannerz found bad cells in the SSD. The owner is replacing the SSD under warranty. He also found his cable was bad. Talk about bad luck!

If I had a link to it, I'd post it but I don't. You could go to MacRumors and search their forums for "Scannerz" and I would think you would find it. Like some of the other posters in that thread, I though SSDs were supposed to automatically correct bad blocks, but apparently that applies only to sectors that have depleted their write ability.

Hope this helps.