What Bookworm has said so far is spot on (as usual!
From an ATC point of view, we do tend to use the Semi-circular rule within controlled airspace in the cruise. Thus 'Westbound' flights will be at even flight levels (260/280/300/320 etc) and 'Eastbound' will be at odd flight levels (270/290/310/330 etc). Once you get above RVSM airspace (above FL410) it gets a little different, but don't worry too much about that. There also some exceptions, for example Brest Control require traffic cruising 'westbound' through ORTAC (near Alderney) to be at an ODD flight level (290/310/330 etc).
Having said all that, the traffic density and internal ATC agreements can mean that traffic actually cruises at the 'wrong' semicircular level for its direction of flight. It's not a huge problem as we have a magic thing called radar which is supposed to help us stop them from bumping into each other..
Quadrantal levels are NEVER used for a cruise level within the airways system.