COD 1 and united offensive used the id Tech 3 engine (= quake 3 engine)
MW2 uses IW 4.0 engine, which is based on the engine for MW1, which is vaguely based on id tech 3, but the difference between id tech 3 engine and IW 4.0 are enormous, and will not be 'linked' by VAC..
Black ops uses a new engine, based on the waw engine, which was based on the mw1 engine, which again is vaguely based on id tech 3.
But again, the differences are so big, it's not comparable.
Hence strafe jumping, many similar commands, and the same general feel.