It's perfectly legitimate to switch tenses as you speak, even within one sentence, PROVIDED that the time frame has changed.
To take an obvious example: "Yesterday I wore a blue shirt but today I am wearing a red shirt." I switch the tense from past to present because the first half of the sentence is talking about yesterday, the past, while the second half is talking about today, the present.
Of course there are more subtle and complex examples. Consider, "I didn't eat lunch yesterday because I have been on a diet." I begin with a simple past because I am describing one discrete event: lunch yesterday. But then I shift to present continuous because the diet is a continuous thing. I didn't just go on the diet yesterday, skip lunch, and then decide to quit dieting. (Well, that's how I usually treat diets in real life, but this is just an example.)
Most of your examples fall into that category: you're shifting tenses because you are, indeed, talking about different time periods. "I told him that I work for HP." "Told" is in the past tense because you are referring to one discrete event in the past. But "work" is in the present because, at least at the time you told "him" this, you were working for HP in the present. The sentence, "I told him that I worked for HP" is potentially ambiguous. Is "worked" in the past tense because you worked for HP at the time you made this statement, but you no longer work there now, when you are telling this story? Or was working for HP in the past at the time you made the statement? Either interpretation is possible and it would take more context to make clear which is meant.
Note that you should definitely NOT switch tenses where there is no change in time frame. Every now and then I read something where the writer carelessly changes tenses for no apparent reason, like, "Yesterday I went to visit my friend Bob. He isn't home. I called him on the phone. He answers and says ..." etc. There's no reason to shift tenses there because all the events are happening in the same time period. At the least it's disconcerting, at the worst it could create confusion over when events happened.