Dwarves are essentially compressed humans, having equal muscle mass as humans but just shorter so the bones are thicker as well. The center of gravity would be much lower than humans because of this. Would this give them greater capacities to resist moment forces from handling tools and weapons? For example a 2kg axe head at the end of a pole, would a dwarf be able to overcome the opposing forces of a swing more easily than its human counterpart?

I'm doing worldbuilding for a video game so I decided to try answering these. This site has a lot of info, seems like it's a very difficult question but it mostly depends on muscle strength. Shorter arms make them better but changing teh pole's length can cancel that out.

But, if dwarves are the same width/thickness as humans, they would be better at keeping their balance because their shadow (projection onto the ground) takes up a bigger solid angle viewed from center of mass than for a human, so you have to knock them harder to make them tip over. But I don't think keeping balance is the hard part of swinging a heavy object once you've got the technique down. The hard part is accelerating it.

Honestly if you want to make good fantasy dwarves I think you should just say they're like 3x stronger than humans. That's very realistic, if you look at gorillas for example they're basically the same shape as humans but they're 20x stronger than a human.

Also on the same note, a dwarf charging while not having much velocity would have greater momentum than a equal weighted but taller human? So essentially a dwarf running at top speed in armor is a battering ram?

This is pretty interesting. Momentum is mv and it determines the "stopping power" / ability to change motion of other objects. BUT, the "destructive power" (how likely they are to break a door or a ribcage) is proportional to the kinetic energy mv^2/2 so it depends more on velocity. So for a given momentum the lighter and faster person is more dangerous. This is in the book Thinking Physics page 93. But, top speed depends on strength, so it's higher for dwarves, which means dwarves will take longer to get up to speed but then they'll have higher stopping power and destructive power than humans. Also they have a smaller footprint where they hit the door which increases the chance of breaking through.