I understand that you already posted this elsewhere, and I answered it there. But just in case you didn't see, I'll paste the same answer here.
(Not a teacher)
A morpheme is defined as 'the smallest linguistic unit that has semantic meaning'. If you cannot 'split' the word any further into smaller parts, then this is the morpheme, e.g. 'the' is a morpheme as there is no smaller unit of meaning within it. 'Unthinkable' has three morphemes - 'un-' 'think' and '-able'. Often, a word with more than one morpheme uses affixes like 'un-' and '-able' here.
A morph is simply the phonetic representation of a morpheme - how the morpheme is said. This distinction occurs because the morpheme can remain the same, but the pronunciation changes.
The best example of this is the plural morpheme in English '-s'. '-s' is the morpheme, but the morph changes in different words:
Cats - '-s' morpheme is pronounced /s/
Dogs - '-s' morpheme is pronounced /z/
Houses - '-s' morpheme is pronounced /ɪz/
These various pronunciations are the morphs of the morpheme '-s'.
This leads onto what an allomorph is. Allomorphs are the varieties of a morpheme, which is closely related to the morph. The morph is just how you pronounce the morpheme, the allomorph is the variation in pronunciation.
So, the morpheme '-s' (plural) has three allomorphs with the morph /s/, /z/, and /ɪz/.
I hope that's clear.