A mouse scammering across the room changes the rotation of the earth, though not in any measurable way. This earthquake and resulting tsunami could not significantly change the angular momentum of the earth as a whole, however, if it redistributed the mass of the earth, it could change both the rotation rate and the rotational axis.
The canonical analogy is the ice skater who spins faster by drawing her arms in towards herself. The actual case is a little more complicated. Leaving out the astronomical effects of nutation and precession (which actually do involve long term predictable changes in the direction of the earth's rotation and hence changes in the earth's angular momentum) the earth's axis of rotation wobbles around its "mean" or conventional point. This wobble is not completely understood, but it is not much different than the expected results of "eulerian wobble". You see "eulerian wobble" every time you see a replay of a pass thrown by Jim Plunket - a not perfect spiral.
The effect is somewhat subtle, one second of arc corresponds to a displacement of about 30 meters on the surface of the earth. For a good discussion of matters effecting the earth's rotation start here
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