What is the most correct way to say: 1 there are other job positions - 2 there are others job positions - 3 there are others jobs positions - 4 there are other jobs positions - 5 there are others jobs positions - ?
Out of your five examples, only the first one is grammatical. That's because you generally can't have a plural noun, the pronoun others (which is just the plural version of the pronoun other) or anything at all that's plural used as a noun adjunct (also known as an attributive noun) or an adjective. Descriptive words describing nouns are usually in the singular in English (that's probably true 99.9% of the time). So, only this one is correct:
There are other job positions.
But let me say that gain: that rule is only true in general. There are situations where a plural noun can be used as an adjective. For example:
My university's Foreign Languages Department.
the cars database
The formation of attributive nouns like those above is really done on a case by case basis as there are no clear rules as to how to do that for any word or phrase in general. This is something that only comes to you as your English-learning experience grows.
1 - "there are other job positions"
In this sentence, both "other" and "job" are adjectives connected to the noun "position." In English, you don't change the adjectives when the noun is plural, so the "-s" suffix is only added to "position."
It may be confusing that "job" is acting as an adjective here, since it's normally a noun. See noun adjunct for more examples of this. If you look at the sentence with that word removed, it might make the grammar of the sentence easier to understand: "there are other positions."