So, I am familiar with the wording on Winter Orb, but recently I learned a mamber of my former play group has been running against a commander deck which runs it. During one of the matches, he was said to be using a Disallow/Stasis ability on other players turns to counteract the orb. Now, I am familiar with Orb, but my question is, the ability on it, state based action or static/world ability? Basically, is this a legal play that the person is doing.

There's a few things to address, here.

First, the current Oracle text for Winter Orb:

As long as Winter Orb is untapped, players can’t untap more than one land during their untap steps.

There's no occurrence of the Trigger keywords (When, Whenever, At), so it's not a triggered ability.
CR 704 lists the state-based actions; this has nothing to do with any of those.
I'm not sure what a “world ability” might be - perhaps a holdover from early “Enchant World” cards, like Concordant Crossroads? - but it's definitely not one of those.
Trivia: Winter Orb was what used to be called a “Continuous Artifact”, which basically meant it only worked if it was untapped. All of those early variants (Mono, Poly, Continuous) have been supplanted with Oracle text.

The effect on Winter Orb is, in fact, a static ability. And CR 604.1 gives us a simple explanation of what that means:

Static abilities do something all the time rather than being activated or triggered. They are written as statements, and they’re simply true.

While Winter Orb has a condition (if ~this~ is untapped) added to its text, it remains a static ability that's either true (if untapped) or not (if tapped).

So, it sounds like your player may be misunderstanding a common Winter Orb “trick”: if you control the Orb, and a way to tap it during another player's end step, you can untap all of your lands, and no one else can.

If, however, they are trying to use Disallow or Stifle (not “Stasis”) to counter Winter Orb's ability, that's not a legal target - because it's neither a triggered, nor activated, ability. In fact, it doesn't go on the stack - it simply changes the rules of the game, if it's untapped.

d:^D