So how can christianity be a monotheism -
You have the God, the son of god, holy ghost, Mother mary, the main angels, satan, many secondary angels and devils, saints and apostles and all of these are supernatural characters in the christian scriptures. Technically [like say the greek gods], these are all gods, right? Of varying powers and varying attributes, but worthy of the tag.
You know Aaqucnaona, that's a subtler theological problem than it sounds. Throughout history, ostensible monotheists have almost always believed in a whole variety of supernatural beings, while insisting up and down that they are staunch monotheists in good standing.
If we define 'god' as 'powerful supernatural being', and if by 'nature' we mean something like 'the physical universe and its contents', then angels, demons and so on would indeed qualify for inclusion as gods.
But I don't think that any of the monotheistic religions would define their monotheistic 'god' quite that broadly, merely as 'powerful supernatural being'. They want to argue that their single monotheistic god is the supreme monarch of the entire universe, it's lawgiver and typically its creator as well.
So in that kind of vision, the lesser supernatural beings can still exist, while still being subject to the highest god's lordship and law. While they might not be physical or natural in the scientific sense, and might inhabit some transcendent heaven or other, they would still be part of the created order.
In other words, monotheistic religion's creation/creator distinction doesn't exactly correspond to the natural/supernatural distinction that modern science recognizes.
And even if thats not true, the trinity is equally god-like in power and attributes, no?
The trinity is a lot tougher theologically for the Christians, since they want to insist that all three are separate divine "persons", while insisting adamantly that they are all one single god. So the kind of simple solution that I just outlined won't work for the trinity.
If so, how are 3 deities 1 god?
There's a late antique formula that was later adopted as the orthodox position, that speaks of three 'persons' in one 'substance'.
Many of the late antique trinitarian controversies revolved around the 'same substance' part ('homoousion'). Some wanted to argue that the three members of the trinity possessed similar divine substance (homoiousion'), but this was condemned as heretical since it threatened to enshrine a tritheist polytheism. (This ancient argument is where our phrase 'one iota of difference' ['iota' is the Greek letter 'i'] originally came from.) So the trinity idea is saying something stronger than simply that the three members of the trinity are all made from generic 'god stuff'. It's numerically one-and-the-same god-stuff.
Or is it like the 'avatars' in hinduism?
Another side of the early trinitarian controversies revolved the 'three persons' part. In ancient classical Greek, 'persona' originally meant a role that an actor played on stage. It was a false-face that he presented to the audience. At the time of the trinitarian controversies, that interpretation would naturally have occurred to most Greek-speaking people. When the idea of the trinity was first appearing, a famous theologian named Sabellius championed the idea that the three 'persons' were just different ways that the one god manifested himself to humanity. Three different ways that one thing can appear, so to speak. But as the Christological controvesies took hold, theologians believed it very important to argue that Christ's death and resurrection were something more than just a divine actor play-acting an illusiory earthly drama. So Sabellianism was eventually condemned as a heresy.
That left theologians promoting a position that sounded like three distinct conscious personalities inhabiting one numerically single divine stuff. And that suggested something like multiple-personality disorder. People in late antiquity wondered, what happens if the three persons of the trinity disagree with each other? So the last stage of these controversies was the 'monothelite' controversy, the question of how many distinct wills the three persons supposedly had. People suggested that while they were three separate people, they only had one will, so were always in perfect harmony. Others attacked that as a return to somethng like Sabellianism, and the arguments continued.
These kind of theological controversies are basically what was replacing older-style Greek philosophy in the 6'th century CE or so, it's what attracted the kind of people who would have become philosophers in earlier centuries, and it's the kind of intellectual life that the early medieval world inherited from antiquity. In the Greek-speaking east particularly, it kind of shaped the whole intellectual contour of Byzantine society and the excruciating subtleties of Greek Orthodox theology.