The phrase "non sequitur" means a conclusion that does not follow from the previous argument or the cited evidence.
For example, suppose someone said, "Bob has been fired from his last three jobs. Bob is not a very good employee." That makes reasonable sense. "Bob is not a very good employee" is a plausible conclusion that one might draw from the fact that he has been fired three times.
But suppose someone said, "Bob has been fired from his last three jobs. Bob is not a very good brother." That makes no sense. It is not at all clear what losing his job has to do with being a good brother. This is a "non sequitur".
In real debates, a non sequitur is often far more subtle. Like in a political debate, someone might say that opinion polls showing a majority oppose a government policy prove that it is a bad policy. Someone on the other side might reply that this is a non sequitur: opinion polls might prove it is an unpopular policy, but that of itself doesn't prove it's a bad idea. Etc.
To say that a person is a non sequitur doesn't make literal sense. A person is not the conclusion of an argument. Someone might call himself a non sequitur as a joke or to make a point. Like your last example: I am a non sequitur because I am here to make no sense. I presume the other examples are in the same vein, but without more context, I can't say.