The Imperium is just trying to survive, yet....
The Imperium is trying to maintain its Empire while continuing the survival of the human race, the triumph over the warp and the destruction of the heretic and the xenos. So everyone else in the galaxy who is not a human. Not withstanding all the people pulling the strings in the backgrounds to achieve their personal goals.
the Eldar are arrogant, holier than though, common-sense lacking space elves who for some reason like to take the most convoluted paths to their goals.
Justified arrogance. They sometimes assume that others will understand their outlook on life [which literally looks at all times of life] and find themselves mistaken. Their Empire was something they had pride in and sit on the same boat the Imperium have, if an old, worn boat.
the Dark Eldar are pretty much the same except they have the added 'bonus' of depraved sexual desires and deviant things that would make even Slaanesh blush.
All Eldar have them, the DE give themselves to them.
The Orks are, well, the Orks.
Technically the happiest race in 40k, it's pure grim darkness is their version of Nirvana. Wherever they go there is fighting to be had. They are the only winners to 40k, all the other races should aspire to their philosophies.
the Necrons are freaky genocidal zombie robots.
Not since Ward slammed his face on them. Now they have leaders with personality, not withstanding Glad0s worlds which are pretty much just that. Assume 3rd edition Star Gods is the more accurate depiction, it has more canon to support it.
In which case Lovecraftian feels are achieved. Probably the most sincere faction of the 40k universe.
[Excluding Trazyn].
the Tyranids are brainless galaxy devouring monsters
Their collective intelligence is strong. Ironically the only thing that separates their ideology from the Imperium's is that the Imperium doesn't leave the worlds they exploit.
the Tau are space communists who want to forcefully convert everyone to their way or kill them all.
They seem to be more of a mix with space Japanese Imperialists and Hindus. Reasonable to the point of naivety. They want an Empire, they want to be a power like the Imperium. They want to make it better than the Imperium and the Eldar's lost Empire, making theirs without their predecessors mistakes, bring their own new flaws into the galactic stage. Kill only those who oppose you directly... Efficiently.
And Chaos loves to take a dump on everyone every once in a while for shits and giggles.
Contrary to some of the recent fluff, chaos has purpose.
Tzeentch - everything is changing. Change is good. Gives people hope [hope leads to chaos].
Nurgle - everything is impermanent. Embrace decay [end the suffering].
Slaanesh - everything sucks. You might as well enjoy sucking [happiness is achieved with amorality].
Khorne - everything bleeds. No matter where the blood flows, it all ends in death [blood for the blood god*].
*Khorne does not like the blood of innocents. He sometimes gets mad when his followers kill the unarmed. They are noble slaughterers.
**Collateral is more acceptable though.Frankly? Yeah, I can blame them. The Imperium can learn a lot from the various species they meet, even if it's only new weapons technology. Instead, they bomb them to oblivion. Remember that they would have wiped out the Tau (a bunch of spear-wielding primitives who barely mastered fire) if not for that freak warp storm. No real reason to do so, they were just in the way.
The Imperium are willing to let Xenos live as long as they pose no threat. There is a story of a guardsman doing very bad things to save an entire species of sub-humans by faking records and saying they're xenos not mutants. Mutants get the purge no matter what, Xenos get a blind eye if they don't go stabbing at Imperials.