OED's entry for to have off, as of March 2015, is (abridged):
to have off
trans. colloq. to have it off rare in U.S. use.
a. Criminals' slang. To successfully carry out a crime, esp. a robbery or burglary. Cf. sense 3. Now rare.
1977 ‘E. Crispin’ Glimpses of Moon xii. 235 He had had it off all right, thanks..to making careful reccys.
b. To have sexual intercourse (with a person). Cf. sense 2.
1982 M. Leigh Goose-pimples ii, in Abigail's Party & Goose-pimples (1983) 151, I know about you two. I know you've been having it off.
trans. colloq. To have sexual intercourse with. Cf. sense 1b. rare.
1970 Irish Times 5 June 7/2 He had her off at that time probably in his hotel at Dungloe, or he had her in a caravan at Bundoran.
trans. colloq. To steal (something); to rob (a person). Cf. sense 1a.
2004 G. Johnson Powder Wars (2005) iii. 32 I'd got into robbing wagons... Mostly they were parked up and we'd just have them off. Sell the vehicle.
The following applies to british-english.
All of thoses senses are common to have it away, and in almost all cases off can be replaced with away. The quote in 1b (→ "I know you've been having it away") sounds rather quaint. Having it off generally refers to sex and is rather more vulgar than having it away. When referring to stealing, have it away is more easily understood than off.
Have it off is almost always sexual. Have it away is usually non-sexual unless the context allows that.
As OED notes, both forms are at best colloquial; in my experience have [it] off is rather more vulgar than using away.