What is offset? my a/v unit shows -4 and -8 depending on mode.
Also what does the term HQ mean.

Offset - No idea without make and model and what control setting you are talking about. Could mean anything but with no context to go on it is impossible to say what it means.

HQ - either means Headquarters (unlikely) or High Quality. Again without knowing the make and model and what setting you are referring to it is impossible to say for certain.

I see this on my denon avr-2310 come up in the display to when it changes to Dolby Digital.

My model is Marantz nr1504 the offset figures show for a couple of seconds in the display when changing from Pro-logic to digital and visa versa.
The HQ is in the audio menu set up.

The answers for this and everything else are in the manual. Download the pdf version and you'll be able to search it by word which makes finding info on the spot much easier.

Anyway, Offset is a volume levelling function that applies to Dolby Digital signals. There's information in a DD signal that tells the amp how loud it is. The amp can use this to minimize the difference in volume when switching between sources. This avoids getting blasted out because you changed to a source where the signal is much louder. The number indicates how much reduction the amp has applied. 0 is no reduction. -1 is a little bit, -10 is a lot more.

HQ is for the signal restorer function. It tries to undo the signal mangling effects of audio compression in the source signal. HQ stands for High Quality and it indicates that the signal isn't too badly messed up in the first place so the amp is applying on a small amount of correction.

Have a read through your manual to see if or how these settings can be adjusted.