Is there a little less oxygen (I mean less by density) in the equator than at the poles?

"Since gravity is a little greater at the poles, does that mean there's also more oxygen there in the atmosphere?"

No. There are many factors which affect air density, but not gravity.

Density of the air is a function of temperature and pressure. $rho sim P/T$

Pressure is the same anywhere at sea level (well, because of movement of air pressure may increase and decrease, but it's not because of gravity). This is because potential energy of any mass would not change if you move this mass along the sea level (otherwise water would flow and sea level would change) => gravity does not affect movement of air along the sea level = > if pressure is different in different areas at sea level the air would move towards area with smaller pressure.

Temperature is different. Temperature on equator is about 20% higher than temperature on pole (+30C vs -30C = 300K vs 240K), so the air density on pole is about 20% higher than air density on equator. Same situation with all the gases which are present in the air.