the problem with this surname is that there are several possibilities, because it can be a variant of two different surnames that are not related, as the above link shows. The Steck surname from the above link is related to Steckler and Stechler. But the variants that you give lead to another group of surnames apparently. And the possible relation with Steg, not to mention, which is a small way, and in this case would also be related to the Dutch surnames Steegh and Van der Steegh.
Stokes (origin: Local) A parish in Buckinghamshire; also, towns in Suffolk and Gloucestershire, England. The name signifies a place, a settlement. Stuge, Danish, a ravine.
Personally, i think that if you found these spelling variants in your own family (when you were investigating your family's history or alike) that the name is related to steg which means 'alley, passage,small way' and that your family is of Dutch origin, because Steagh resembles Steegh close and Steach resembles Steech (which itself is not used anymore, but Versteeg was often written as Versteech way back). And Stegh is often used as a variant of Steegh or Steeg. In time, it probably has changed in Steck and Stack under influence of the English language and the presence of Steck in England as a variant of other surnames. It used to more that people changed their lastname to something that resembled it, that was already an existing surname, but that was not related, like Steck as a variant of Stokes or Steckler, and so it became a variant of Steagh and or Steegh, et cetera. I hope this helped.