Is it possibly this?
Containing the books The Reality Dysfunction, The Neutronium Alchemist and The Naked God
Written between 1996 & 1999
There are two human factions the Adamists and the Edenists, though they are spread out over the galaxy not just the solar system. It opens with an attack on an asteroid mining facility using banned anti-matter bombs.
... involved a futuristic war between two opposing humanoid factions that have settled various planets in the solar system
There are a number of alien species that are around the periphery of the story but not involved in the actual conflict between the humans.
... remember there being aliens as well, but I'm fairly certain they weren't involved in the conflict
One of the protagonists pilots a ship called the Lady Macbeth.
I believe one of the factions piloted a starship named after a famous person in history
Dead spirits inhabit the bodies of humans and the main plot point of the story revolves around this possession and the quest to end it. The leader of the possessed is the spirit of Al Capone.
I'm pretty sure several of the humanoids joined together in a massive orgy to celebrate the banishment of some kind of spirits
There is copious amounts of sex throughout the three books so an orgy would not be out of place.
Each book is a tome containing many hundreds of pages.