Can high energy galactic neutrinos harm us? The neutrinos that are generated from the supernova are in the order of Peta eV, which is very large; when they reach the earth surface and get contact with earthly bodies, do they make any harm, if not why ? 
 A: Here's a relevant "what-if?" article. It cites a paper by Andrew Karam : "Gamma and neutrino radiation dose from gamma ray bursts and nearby supernovae" .
According to this paper, the neutrino radiation dose at a distance of one parsec from a supernova would be around half a nanosievert. At $2.4 \mathrm{AU}$, the radiation dose from neutrinos alone would be lethal ($\mathrm{4 sieverts}$).
If Spica (one of the nearest stars to the Sun that has enough mass to end its life in a Type II supernova) went supernova, we would get about $ 4 Sv ⋅ (2.4\mathrm{AU}/250\mathrm{ly})^2 ≈ 100 \mathrm{fSv}$ of neutrino radiation. This represents less than 4 milliseconds of the average background radiation.
From the paper :

The  average  energy  of  neutrinos  released  in supernovae
  explosions is between 5 MeV (Schramm and Brown  1990)  and  15  MeV 
  (Sutaria  and  Ray  1997).

It's not clear where your $\mathrm{Pev}$ order of magnitude comes from. Scaling the previous quantity by $\mathrm{1PeV/(15MeV)}$, the neutrino radiation dose would be around $6 \mathrm{µSv}$. This quantity would be perfectly measurable but not harmful.
Neutrinos are extremely hard to detect, it makes sense that even highly energetic neutrinos from a few parsecs away would not interact with our body in any way.
The effect of other particles from a near-Earth supernova would be much stronger and potentially dangerous.
A: This is a "knock me over with a feather" scenario. Even moles and scientific notation would have a lot of trouble calculating the amount of neutrinos required to even interact with one of our atoms. (We're assuming all of them hit space somewhere in your general volume.)
