universe - Is the earth bombarded equally in all directions by neutrinos?

In addition to neutrinos from the Sun and other discrete sources in the Universe (see James's answer), there is also expected to be a cosmic neutrino background. Although this is yet to be detected (efforts are underway), its expected properties are reasonably well understood. The neutrinos "decoupled" from the universe seconds after the big bang at temperatures $>10^{10}$K. As the universe expands, the de Broglie wavelength of these neutrinos (which are not massless) lengthens with it, such that the neutrinos are expected to have a temperature of $<2$K today. There are 112 of these cosmic neutrinos per cubic centimetre per neutrino flavour (probably 3).

The C$nu$B is analogous to the cosmic microwave background in a number of ways, but (a) it hasn't been detected; (b) it is cooler; (c) because neutrinos have a small but non-zero mass, the C$nu$B neutrinos are likely non-relativistic today.

This latter point is important to your question. On large scales we expect the neutrino background to have an asymmetry due to the motion of the Earth through the universe with respect to the co-moving standard of rest. This is exactly the same global dipole asymmetry seen in the cosmic microwave background. However, non-relativistic neutrinos are also anisotropic because they are much more affected by gravitational fields. In particular they should be gravitationally focused by the Sun, such that the Earth receives more neutrino flux when the Earth is "leeward" of the Sun with respect to its motion with respect to the co-moving rest frame. This will produce an annual modulation in any non-directional neutrino flux amplitude of a few tenths of a per cent (Safdi et al. 2014) and might allow a dectection of the C$nu$B to be confirmed.

On top of this there may be other anisotropies caused by the acceleration of C$nu$B neutrinos by massive galaxies and clusters of galaxies, that should lead it to be much more inhomogeneous and anisotropic than the cosmic microwave background. Overdensities with respect to the average of factors of 10 or more are possible (see section 2.2 of Yanagisawa 2014), but it depends on exactly what the neutrino mass is.