ず is the continuative form (連用形) of the negative auxiliary ぬ. It follows the pre-nai/irrealis form (未然形). In other words, ず and ぬ are different conjugations of exactly the same word. (Note that when ぬ follows a continuative form, it's a different auxiliary for perfective aspect that conjugates differently.)
The difference between ぬ and ず is simple; ず modifies something adverbially, whereas ぬ modifies something attributively (aka adjectivally) or works as a predicate. So 有無を言わせず is "forcibly"forcibly and 有無を言わせぬ is "forcible/undoubtable/indescribable"forcible, undoubtable or indescribable depending on the context (literally, "which;(which) doesn't let [someone] say yes or no").
言わせる (ichidan) and 言わす (godan) are two causative forms of 言う. They mean the same thing, although 言わせる sounds more common in ordinary speech.
So we have the following combinations:
連用 (adverbial) | 連体 (attributive) | 終止 (predicative) | |
---|---|---|---|
言わす | 有無を言わさず(に)働かせた働かせる 有無を言わさないで働かせた働かせる |
有無を言わさぬ迫力 有無を言わさない迫力 |
彼は有無を言わさぬ。 彼は有無を言わさない。 |
言わせる | 有無を言わせず(に)働かせた働かせる 有無を言わせないで働かせた働かせる |
有無を言わせぬ迫力 有無を言わせない迫力 |
彼は有無を言わせぬ。 彼は有無を言わせない。 |
Related: What is the difference between the negative forms -ず and -ぬ?