Most of the newer HDD recorders, will allow you to do the first three actions. "turn on Sky One, record Twenty Four, edit out the commercials"
However, none that I know of can encode the recordings into the DivX format. (I may be wrong on this, try posting a message here > click here < in the DVD Recording forum) If I am correct, you will need to record the episodes onto DVD, using a DVD recorder. (Either built into you HDD recorder, or standalone).
Transfer the DVD video to your computer, where you should be able to find programs to convert DVD files in DivX files. Then once in DivX, write them back to a DVD.