Nicholas isn't HOF worthy, neither is Damphousse.
Andreychuk deserves it. So do Tkachuk and Turgeon.
Here's the thing. When they were playing, Nicholls and Damphousse were WAY better players than Andreychuk.
Nicholls and Damphousse both had quite respectable longevity as well, even if they didn't play for 22 years or whatever.
None of these players was great defensively or physically, but Nicholls and Damphousse were far more well-rounded, skilled players than Andreychuk.
Nicholls and Damphousse both led multiple franchises in scoring. Damphousse led 3 Canadian franchises in scoring, in fact (maybe the only player ever to do so?). Nicholls was a 3 x 100+ point scorer, who once finished only 18 points behind Gretzky in the 1980s. The following year he was outscoring prime-Yzerman for most of the season.
These kind of players' (respectably long) primes are WAY, WAY beyond the ability of Andreychuk, whose game basically consisted of getting to the front of the net and banging in rebounds, at which he was very good.
Saying Nicholls and Damphousse don't deserve the Hall while Andreychuk does, is like the modern-day equivalent of saying that Backstrom doesn't deserve to be in, while Patrick Maroon does.
Having said all of that, if I had my way, none of the players you listed would make it in.