Aloha particles leave an ion behind. However, it is the nuclear process rather than the ionization one the process that is studied. When an alpha particle passes near an electron orbital, the particle will probably take that electron indeed. That is a very important property of alpha particles: they are very electronegative and tend to take any electron near them. That is why they are so dangerous: because they take the electrons out of your skin and leave you burnt. 

But, why are they Helium nuclei? Why not Oxygen? 

In fact, it is because of the stability of the Helium nucleus. If the atom lost a Lithium nuclei this nucleus would get rid of two protons to become more stable, so that you end up with an alpha particle.