I'd happily use "He flogged them off cheap" to mean exactly the same as "He sold them off cheap". Using "flogged off" is slang and I see it as more dismissive. Unlike Glasguensis, I do see "to sell off" as implying "to sell things cheaply because you want to get rid of them". If I heard that a shop was selling off its stock, I'd expect there to be signs in the windows offering discounted prices.
I see "to sell off" as meaning to sell something for "less than it's true value", which isn't necessarily the same as "cheap". I could sell off the antique cutlery at 90% of its valuation. I also might sell something off at auction, where it might actually fetch more than its valuation. It implies that I am obliged to sell it to raise money. To flog, on the other hand, implies to me that I have to convince people to buy the product, usually by offering it at a low price.
We're dancing around shades of meaning. When I say "sell/flog something off" means "sell cheaply", I mean below normal price. When I say "sell/flog something off cheap" I mean considerably below normal price. As a generalisation, I see no shade of meaning between "sell" and "flog". One is standard English, the other is casual slang. If I was selling the family silver I'd be unlikely to use slang, so I'd sell it off. However, Gordon Brown flogged off the country's gold reserves without any need to convince anybody to buy. That's an example of using "flog" pejoratively - if I had used "sold off" some people might think I thought it was a good idea.
The BBC has an extremely popular antiques programme called "Flog It!" which has nothing to do with selling antiques at below their true value. They are happiest when items go above the estimate.