Without going into great detail, "standing" basically requires that you have been or will be harmed by something that the court you have chosen has jurisdiction over and that a decision by such court in your favor will redress your harm ("fix your problem") to some degree. In most cases, standing is easily satisfied, but can be tricky in constitutional challenges. I'll let the current law students discuss it more, if they want.
I'm not sure if you have a particular case in mind, but to answer what I think you're asking about, filing a civil suit against someone in, say, a Texas District Court, is generally not affected by being an illegal immigrant or having been accused of, arrested for, or even convicted of a crime. As long as you have an "injury", one or more causes of action that fit, meet the amount in controversy, venue and any bond requirements, you're probably good to go.
Being here illegally has nothing to do with it. Bringing up the issue as the defense is a good way to get your ass slapped on appeal, should you win at trial.
