Post metal and avantgarde metal are experimental. As Uldreth said post metal is a derivation of post rock, which initially was quite experimental in its use of usual rock instrumentation but put to use in unusual song structures atypical of those found in rock. As I understand it was about stripping the genre down to its bare essentials or to its foundations which are the instruments and then rebuilding the structure from the ground up, writing songs that used rock instruments but sounded nothing like rock. To confuse things you might describe that as avantgarde in approach.
Post rock, and by extension post metal, was experimental and avantgarde initially and proved to be influential enough to spawn itself a genre of music. As bands that play post metal arise they can be generic and do little to further the style, their artistic motives having less to do with the same kind of inspiration which the likes of Isis or Neurosis had in establishing a set of characteristic elements which others have caught onto and attempted to replicate or imitate.
Post has more definite generic traits than avantgarde, vague as they are I suppose.
I think of avantgarde as less of a genre and more as a broad collective of innovative approaches which push the boundaries of particular metal subgenres and/or metal itself as a genre. These approaches usually come from a range of sounds, from playing around with death metal structures, black metal structures etc. You'll find some avantgarde bands imitating or borrowing the ideas and approaches of others which leads to a loose sense of a genre, or at least much looser and broader in scope than is largely the case with post metal.
Experimental metal, as has been said already isn't a genre, it's used to indicate that what a band plays and how they play it involves some sort of creative feature not used or infrequently used before.