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][1]. (Note that when ぬ follows a continuative form, it's a different [auxiliary for perfective aspect][2] 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" and 有無を言わせぬ is "forcible/undoubtable/indescribable" (literally, "which doesn't let \[someone\] say yes or no").

言わせる (ichidan) and 言わす (godan) are [two causative forms][3] 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<br>有無を言わさ**ないで**働かせた | 有無を言わさ**ぬ**迫力<br>有無を言わさ**ない**迫力 | 彼は有無を言わさ**ぬ**。<br>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<br>有無を言わせ**ないで**働かせた | 有無を言わせ**ぬ**迫力<br>有無を言わせ**ない**迫力 | 彼は有無を言わせ**ぬ**。<br>彼は有無を言わせ**ない**。 |

Related: https://japanese.stackexchange.com/q/235/5010


  [1]: https://www.kokugobunpou.com/%E5%8A%A9%E5%8B%95%E8%A9%9E/%E3%81%AA%E3%81%84-%E3%81%AC-%E3%82%93/
  [2]: https://japanese.stackexchange.com/q/12585/5010
  [3]: https://japanese.stackexchange.com/a/86621/5010