Irregular plurality situations in English

Solution 1:

This question is actually quite broad. Irregular plural forms can arise for a variety of reasons. Wikipedia has a huge section on the subject, with six subsections: "Nouns with identical singular and plural", "Irregular -(e)n plurals", "Ablaut plurals", "Irregular plurals from Latin and Greek", "Irregular plurals from other languages", and "Words better known in the plural".

Wiktionary has a list of English nouns with irregular plurals.

Lastly, there are nouns that (depending on context) can be countable and uncountable, e.g. water, cheese, or email.

Solution 2:

The largest category of non-inflected English plurals are common animal names, although this is not particularly predictable (sheep, deer). There is also a related class which use both an inflected and an uninflected form (fish/fishes), of which in some cases the uninflected form is only used in collective situations: six elephants, a herd of elephant, but again, they need to be learnt case by case. This form seems to apply most commonly to game animals. See also "head" in "twenty head of cattle".