I think there are really three questions that need to be answered for this to make sense:
- is there a "normal" limit to how large a star can be?
- how can population III stars form with such large masses?
- how can population III stars retain their large masses?
An answer to the first question is tricky. We expect large stars to be rare, and the largest stars to be the rarest. On top of this, they'll lead the shortest lives. Getting observational constraints has thus been tricky. There might be a limit to the amount of mass that is available to turn into stars when they form. As for the "normal" limits on the masses of stars, most (as far as I know) involve around pulsational instability. But the recent discovery of massive stars in and near the cluster R136a suggests that stars with masses over 150 solar can form even in material that has a non-negligible metal content. So whether there is a "normal" limit is open question.
The second question is much better understood, thanks to a lot of numerical work. Tom Abel recently wrote an article for Physics Today that summarizes current understanding of pop III star formation. Basically, the smallest amount of gas unstable to collapse under its own gravity, the Jeans Mass, increases with temperature (like T3/2). So the cooler the gas can become, the smaller the fragments we expect to see. What determines how cool the gas can become? The atoms and molecules that radiate within it, and whether this radiation can escape. In metal-polluted gas, various molecular and atomic lines allow the gas to cool to tens of K. In metal-free material, the most effective coolant (in terms of the low temperatures it can achieve) is molecular hydrogen, which will only cool to around 200 K. This is a higher temperature, so we expect more massive fragments. This is a gross simplification! The situation really involves complex dynamics, shock formation, and all sorts of other stuff. Even the question of whether or not molecular hydrogen can form is contested.
Finally, if a massive pop III star formed, would it keep its mass? We know that the some massive stars in the local universe, like Eta Carinae, are violent beasts. This kind of episodic, pulsational mass loss could be present in Pop III stars, but since such mass loss is so poorly understood, this is often ignored. More generally, we expect that the metals in the atmospheres of massive stars absorb enough of the radiation created inside the star to be driven away in a wind. Again, there aren't any metals in metal-free gas, so we expect this effect to be much smaller in Pop III stars.
So, we expect Pop III stars to be larger because there is more gas available, because the gas fragments less owing to its higher temperature, and because we don't think the stars lose as much mass as modern stars do. And, we aren't even sure that there's a limit on how massive stars can be in the first place!
You need to know the equation of state for the star's interior. Once you know this you can calculate the density variation with depth and the gravity inside the star.
Google for something like "star equation of state" to find lots of articles on the subject, but note that it's exceedingly complicated because there are so many factors at work. This is the sort of article you'll find: good luck reading it!
Note also that while we can use models to calculate equations of state, the results are only as good as the models. It's hard to know how good our models are when all we can see is the surface of the star.
Best Answer
The nuclear fusion that powers stars has little to nothing to do with electrons. In the cores of stars, temperatures are high enough that all the electrons are stripped from the nuclei, leaving a pure plasma.
As stars contract and condense out of interstellar dust, their gravitational potential energy is converted to heat faster than this heat can be radiated away. Once the temperature reaches roughly $10^7\ \mathrm{K}$, protons (hydrogen nuclei, stripped of their electrons) have a nonnegligible chance of sticking together when they colide, with one of them converting to a neutron along the way: $$ {}^1H + {}^1H \to {}^2H + e^+ + \nu_e. $$ This is the first step of the PP chain, and it releases energy. There are more steps that ultimately turn four protons into a helium-4 nucleus. In more massive stars than the Sun, there are other ways (e.g. the CNO cycle) to catalyze this process with the help of carbon, nitrogen, and oxygen.
In any event, there is nothing extreme about the gravity. It just happened to pull matter from a huge distance close together. If you took infinitely spread apart particles totaling mass $M$ and formed a uniformly dense sphere of radius $R$, the gravitational potential energy released would be $$ \frac{3GM^2}{5R}, $$ about half of which you expect to go into heating the material. Once hot, hydrogen naturally forms helium in exothermic processes.
Stellar reactions are self-regulating in the sense that if the rate of fusion increases, the additional luminosity would push the outer layers of the star, causing the star to expand and cool, thus reducing the reaction rate. Thus as long as there is hydrogen in the core, stars more or less burn at a steady rate once ignited.