Cloning MIDI drums

This is common when you layer similar samples of any type, but especially drums and percussion. It literally is "phasey-ness", due to comb filtering caused by two spectrally-overlapping sounds.
 
The best way to get rid of it is by simply not layering sounds that are very similar. For example, if you want to fatten a kick drum by using two samples, EQ them so that they have less spectral overlap. 
 
Sometimes, you can further mitigate the effect by shifting one of the samples forward or back by a millisecond or less, so that they are in better phase with one another. This doesn't always work, though, because frequency-rich sounds such as drums often can only be forced into phase at the fundamental frequency and its harmonics. Higher, nonharmonic overtones may remain badly comb-filtered.
 
Intermodulation distortion can also be a problem whenever you mix sounds that are close but not quite in tune with one another. The fix is the same: reduce the amount spectral overlap between the layered sounds.
 
In any case, you usually can't get away with it on a full drum kit. You have to fix each instrument individually.