Even and odd flight levels generally are in accordance with east-west directions as agreed by State authorities in ICAO forums.
One exception is a Flight Level Allocation System, which gives more Flight Levels in a particular direction to enhance capacity of the system. See the example given by Carbide Finger.
The other exception is in the case of a generally North-South route, which sometimes bends a little to the east, at other stretches a little to the west. It would be silly to change levels every other 40 miles or so. Therefor the responsible authorities (that is not ICAO, but the ATC authority of the State or group of States) decide which level to use for that complete route or at least a longer stretch of that route. The route from (beyond) Paris to Scandinavia is an example, the normal level change to an odd Flight Level is just south of the SPY area after flying many miles a bit eastbound. For tactical reasons controllers may co-ordinate and agree to put the level change for an individual aircraft further north or further south, whichever is most convenient to reduce workload and enhance capacity.
In non RVSM the rule cannot apply because of the 2000' separation.
The ICAO rules are clear, odd for eastbound and even for westbound. But local circumstances require exceptions, for good reasons.