Is the earth bombarded equally in all directions by neutrinos? Perhaps it is hard to known for sure because neutrinos are very difficult to detect, although they do go through the earth in very large numbers. But are they passing through the earth equally from all directions or is it really depending on particular events in the universe. It's probable that the sun generates a lot of them, so perhaps in the daytime we receive more of them than at night. But besides the sun's radiation, are the neutrinos coming from everywhere? Or is it possible that the majority of them comes from one direction, and perhaps even has an influence on the earth's movement?
There are only two types of neutrino source that are "bright" enough to be reliably detected. The sun and nearby supernovae. 

The source of solar neutrinos is nuclear fusion, which is also the source of most of the star's energy. Neutrinos also spread out in all directions, so their intensity follows an inverse square law. So the amount of neutrinos is proportional to the brightness of the star. With current detectors no star is bright enough to be observed except for the sun. Other stars do produce neutrinos, and stellar neutrinos come from everywhere (probably more from the milky way) but there are not enough of them to be detected.

Supernovae in the milky way and neighbouring galaxies produce ridiculous amounts of neutrinos, and a spike in neutrinos was observed from SN1987A the closest recent supernova.

Since the sun is the brightest source of neutrinos you might think that the Earth would block out neutrinos during night. However, neutrinos pass right through the Earth almost without noticing. The Earth is transparent to neutrinos. So we detect as many neutrinos at night as during the day.

One thing is certain, there is absolutely no effect on the Earth's rotation or anything else from neutrinos, they just pass right through.