Is a DIY neutrino detector feasible? How long does a neutrino detector filled with distilled water need to be to pick up neutrinos from one direction at about the level of a distant star within our galaxy?
Would an off the shelf avalanche like this work at the end of a silver-plated water filled glass tube?
Assuming you could get it straight enough could a fiber-coupled avalanche diode used for fiber optics like this work for a single pixel of resolution at that amplitude?  How long would it need to be if so?
I know neutrino detectors are typically very large - I'm curious if it is possible to make a single-pixel (and cheaper) largely directional detector by making it very thin, straight and long.
 A: There are a few difficulties in building Neutrino detectors. First and foremost, Neutrinos only rarely interact with ordinary matter. For a neutrino to have an effect on ordinary matter, it has to strike the nucleus of an atom. Unfortunately, atomic nuclei are ridiculously small in comparison to the atom itself - by diameter, the atomic nuclei is about a million times smaller than the size of the atom itself. By volume, it's around one billion billion (10 to the 18th power) times smaller.
Neutrinos hit solid chunks of matter about less often than a particle of light strikes a piece of dust in a nebulae in space. It happens, but you need huge amounts of matter for it to happen. Nebulae are light-years across, with only a few motes of dust every meter. If you could somehow see neutrinos, the earth would look like a particularly faint, spherical, nebulae (if it could be seen at all).
If you built an extremely long detector (preferably hundreds of meters), you would detect neutrinos on rare occasion. But because the rate of neutrino detection depends on how much matter you are observing, and less on the arrangement of that matter, it'd just be more efficient to build a giant sphere of matter, carefully measured for neutrinos.
This brings us to the second problem. When a neutrino hits a piece of matter, it releases a small amount of energy. A neutrino detector is mostly just a giant chunk of matter, and some detectors that can sense those small bursts of energy. But lots of other things also cause small bursts of energy. The only way around this is to block everything that isn't a neutrino. Thankfully, this is relatively simple. Pretty much everything blocks anything that isn't a neutrino. That's why they often build neutrino detectors in salt mines or other underground, highly insulated places: you could spend millions of dollars building a huge concrete pile of stuff to block 99.9999999% of everything that isn't neutrinos, or you could just built it underground.
What you're proposing is possible (linear detector), although you couldn't fit it on a desk...
A: 
The highest flux of solar neutrinos come directly from the proton-proton interaction, and have a low energy, up to 400 keV. There are also several other significant production mechanisms, with energies up to 18 MeV. From the Earth, the amount of neutrino flux at Earth is around 7·10^10 particles/cm2/s.

Neutrinos from the sun have been seen in the Kamiokande detector

To detect charged particles, the KAMIOKANDE detector utilizes Cherenkov radiation in the water. Cherenkov radiation is generated when a charged particle pass through the matter with velocity greater than that of light in the matter. Cherenkov photon is detected by the 20"PMT which is attached inside of the water tank. Owing to a total of 2140 t of water, KAMIOKANDE can detect rare events such as a nucleon decay and a neutrino event

The photons are  created by electrons generated by neutrino interactions:

In a neutral current interaction, the neutrino leaves the detector after having transferred some of its energy and momentum to a target particle. If the target particle is charged and sufficiently light (e.g. an electron), it may be accelerated to a relativistic speed and consequently emit Cherenkov radiation, which can be observed directly. All three neutrino flavors can participate regardless of the neutrino energy. However, no neutrino flavor information is left behind.
In a charged current interaction, the neutrino transforms into its partner lepton (electron, muon, or tau). However, if the neutrino does not have sufficient energy to create its heavier partner's mass, the charged current interaction is unavailable to it. Solar and reactor neutrinos have enough energy to create electrons.

In super Kamiokande , they report with 50000 tons of pure water 5000 events in two years. You can do the numbers for your experimental setup. You would have to wait very many years. In addition the cheap diode will not do. In SK they have photomultipliers, i.e. single photons are amplified to get a signal. A cheap photodiode works with many photons.

Disadvantages of photodiodes compared to photomultipliers:
  
  
*
  
*Small area
  
*No internal gain (except avalanche photodiodes, but their gain is typically 10^2–10^3 compared to 10^5-10^8 for the photomultiplier)
  
*Much lower overall sensitivity
4.Photon counting only possible with specially designed, usually cooled photodiodes, with special electronic circuits

  
*Response time for many designs is slower
  
*latent effect

So the answer is no, one cannot have a cheap DIY neutrino detector.
