There is very little written about this surname.

There was/is a house in Leniz, Guipuzcoa (1448).

The authors note that it could be a variation of the name Ostiz, which originates in Navarre and in Uruguay. But as you note in your request their can be many variations. Those with Basque origin closest to the pronunciations you mentioned are Oste, Ostecain, Ostei, and those beginning with "a" as well. It is possible that there could be common connections between the names, but all appear to stand as different surnames as well (what I mean is that they have original houses in different places). Since you ask - the very best advice that I can give as far as coming to know about your particular family is once again - to begin with what is known and work backwards through the various spelling errors and changes until you arrive at one of those original houses or some other place. I don't mean to be evasive - but this is not an exact science and there is really no way to tell what is differences in original surnames and what is common error without extensive research.