Why would you want to use this in water? For one thing, unless the water was 100% pure (and if it is 100% pure, why are you filtering it?), you would get an electric current flowing betwen the two electrodes (and even with pure water, it is partially dissociated into H[sup]+[/sup] & OH[sup]-[/sup], so a current could flow at sufficient coltages). This wouldn’t charge the particles in the water effectively, although you might well get any negative ions being deposited at the anode & plating it, and Hydrogen given off at the cathode…not the intended reaction). ie it wouldn’t be an electrostatic precipitator because a current would flow.
In addition to that, it costs money to use electricity, why do this when existing filtration sytems already exist for water? Ranging from the simple grill to remove large particulates (shopping trolleys, grit, fish etc) to water through varying grades of sand over a gravel bed - the water passes through the spaces between the grains of sand, but any particle larger than the spaces is left behind. Filtering slows down the flow of water & any water treatment plant will want to get maximum through put for the size of the installation (& I don’t work in the field, but I taught science & did enough field trips 
- I’d welcome corrections by any engineers in the field, or news of any groundbreaking research). They use chlorine to kill any living organisms, but filtering down to HEPA standards would be costly and slow. It can be done & would be on a small scale for when absolute purity of the water is essential - perhaps for clean room processes, but in which case, distilling the water is simpler to do & more certain.
With regards to the oil, I have no information, apart from to say that I doubt that it would work, for the same reasons as the water does not. If you did have ions from it turning acidic in there, it would make a circuit & you would have the same problems. Plus, unless it is a totally sealed system, with no air in & no vapour escaping, depending onthe volatility & ignition energy of the oil, even if it was kept to static electricity, I would be very wary because of the possibility of sparks…
Regarding the radiation filtration, you might get it to wrok for the electrons…since the positive electrode is usually the grounded one. However, the alpha particles are as you said, Helium gas by another name, and whent he precipitator is tapped to drop the dust off, these will just move away as gas particles, even if they were lacking enough energy to cling rather than rebounding in the first place.