If I could describe Shin Megami Tensei, it would be like if Fallout and Pokemon had a baby, but it was raised by Dungeon Master and Pokemon. I guess you could say Fallout was a surrogate mother (well, aside from the fact the MegaTen franchise predates both Fallout and Pokemon, I'm just doing this for frame of reference). Its paternal aunt and uncle would be Snatcher and Metal Gear while its maternal uncle and aunt would be Mad Max and Poltergeist. The child was also raised on the DC comics multiverse, mostly on Uncle Snatcher and Auntie Metal Gear's behest.
From this upbringing the child came to dream of a post-apocalyptic, supernatural, cyberpunk dystopian multiverse with a convoluted, yet minimalist story that's loaded with dungeons crawls and the demons? Gotta catch them all.
Each universe has multiple endings too, creating more dystopian timelines and universes because surrogate mother Fallout impressed upon the child that war never changes. Auntie Metal Gear disagrees on that point insisting war has changed.
Mama Dungeon Master is also a devil worshiper that believes in unchecked freedom while Daddy Pokemon is a controlling religious fundamentalist. Despite the nasty divorce, they'll encourage the kid to talk to angels and demons in order gain more allies and become stronger. They do this in hopes the kid will choose one of them and help them decide the future of the world and rule it. Or you can tell them both to go to hell.
This is Shin Megami Tensei... though sometimes the cyberpunk and apocalypse parts come and goes as they please.
As for the continuity... its complicated. Best to take it one game at a time and worry about the details of the larger story later. Or you can browse Hardcore Gaming 101's
gradually-updated SMT site that does a great job of providing a synopsis of most of the games in the franchise. Those Persona kids have their own universe and split dimensions within this, but that's really its own thing now.
So we have a supernatural, cyberpunk post-apocalyptic world. How you behave will determine your alignment and the ending. SMT isn't as wishy-washy about alignment as something like Mass Effect can be - once you've set your path pre-endgame, it will affect potentially the endgame and the ultimate outcome. Its the classic Law/Neutral/Chaos setup, which has been known at times to be repped by the colors Blue, Green and Red respectively.
Mass Effect was born to Time Crisis and Star Wars across the street and might have been invited over for slumber parties, influenced by some of this and thought Mama Dungeon Master was a total MILF.
I'll be winding down SMT Nocturne later this week, so I'll have a bit to say about that later.
LOOK WHO CAME: