Yes, injectors can be serviced. There are several places that do it. Mr. Injector (
Mr Injector - Home) is a good option, and for $17/injector (roughly) it is a good use of time and money. Just pop them in an envelope and send to him with a form (and credit card #). It's hard to effectively troubleshoot when you have a lot of components about which you're unsure, including injectors.
Have you checked your vacuum hoses? If they're misrouted or if you have vacuum leaks you can get really rough running as well. I didn't see what year car you have. Here's a reference for lots of good info. Look down the page for vacuum hose layout for a 2.0 for your car:
Jeff Bowlsby Tech Notebook.
Just for reference, here's a picture of a CHT on an engine without the tin. It is just to the right of the #3 spark plug. You won't see it, but you can see the wire lead coming out of a hole in the tin. It may not solve all or any of your problems, but it is a part that definitely can cause problems and a variable that can be eliminated (assumes the wiring is good on it too).