Most of the anisohedral tiles that have been found are 2-anisohedral. Here is one criterion for a (usually) 2-anisohedral tile. You can see a summary of the 2-anisohedral tilings that I have classified. I have included the first 3-anisohedral and 4-anisohedral tilings that were discovered. Joseph Myers' webpage shows many more anisohedral tilings, sorted into what order anisohedral tiling they are. On May 21, 2002 he and I discovered a tile that is unbalanced.
If you know of any other anisohedral tilings, please tell me! Or if I have not given proper credit, let me know. See the bibliography for references of where my information came from.