I can't find any information on Avieller - it doesn't get a single hit on Google, so the chances are that your parents made it up.
A similar name is the Jewish male name Aviel, which means 'My father is God'. Aviel is a spelling variation of Abiel
(click on the Abiel
hyperlink for details).
More info on Aviel: http://www.hebrewletters.com/item.cfm?itemid=59
It's possible that your parents heard the name Aviel and made your name up from it. Other names that could have evolved into Avieller (click hyperlinks for details):AvalineAvelineAverillAvilaAvivaHope
that helps :-)
♦ Chrisell ♦
All we have to decide is what to do with the time that is given us. - J.R.R. Tolkien.