Do objects that are invisible to the naked eye occlude much of the stars to Earth based observers? I was looking at a star recently and some other object that appeared to be stationary in relation to the star was occluding the light to only one of my eyes. This is why it caught my attention.

I was able to move my head around this shadow and see the star but there was a definite tiny area where the star was clearly hidden. The object hiding the star also appeared to be a similar size to the tiny point of light of the star. Is this common to observe?

For the last few days I have been asking myself how many objects could be hidden like this (though most with shadows that engulf the earth); How thick are asteroid belts etc, that are between our eyes and the rest of the stars.

Is most of it hidden?
From your description, an object that blocks out light from a star in only one location cannot be an astronomical object.

Occultations by asteroids are fairly common. You can see a list at  http://www.asteroidoccultation.com/. When a star is being occluded by an asteroid there will be a fairly narrow strip from which the star will be hidden. But it is still about 50km wide. The star appears to rapidly fade, and it remains hidden for at most a few seconds, then reappears. Your description of "only hidden to one of my eyes" doesn't fit an asteroid occultation.

The object hiding the star must, therefore, have been local, and not moving. It would be speculation to suggest what it could be.

There are may objects that are hidden in visible light, not by asteroids, but by interstellar dust clouds. We can see them by using other wavelengths.