Thought: Don't give anyone any proper gods except humans. Make gods a uniquely human thing and give the other races an entirely different outlook on the spiritual aspects of life
Dwarves: ..... I'm utterly flumoxed about what sort of gods to give them
In a word don't. Give them great philosophers, teachers and wise men. Call their doctrine "the pilgrims of the inner light". Through suffering we become both more and less than we are
I think that the human gods need to be a rough admixture of defiant resistance/military leaders (think Joan of Arc or Churchill), megalomaniacle conquerors (Caesar, Alexander and Napoleon) and racist genocidal lunatics (whose name need not be listed here). These are the kinds of figures that humans under these conditions would exult.
Halflings: ... trouble-making gods representing the ideal. No clue at all who these gods are, though.
What kind of trouble makers are we talking about here?
The Joker?Or the Joker?
In the case of the latter then a good place to look for inspiration is in works like "a clock work orange" or any of the Taranteno films (I can just envisage reservoir dogs with halflings). One thought is instead of gods give the halfling boogeymen; Uniquely horrific unkillable post-humaniod monsters that are part urban myth and part real.
The bloody reaper: A being of darkness that possesses mens' shadows and drives them to become bloodthirsty knife wielding murderers that prey on women.
The unseen horror: a figure that hides in people vision and can jump from person to person when they make eye contact. It slowly gets closer to you until you notice it then it hides and seeks a new victim. If it gets to you then it will seal your sight. Look it directly in the eyes however and it will take your life or your mind
The Graloon: A hideously burned halfling with grotesque elongated limbs and boneless joints. It drags people into water and drowns them. If someone kills it then they are fated to become it.
The innocence thief: A fiend that take the guise a charming and handsome or beautiful halfling. It shows up where an "innocent" halfling has been lynched. It first befriends and then steals the children of the perpetrators who are never seen again.
As for elves beyond their emperor I could well imagining them adhering to something akin to Confucianism, its either that or to raise the fine art of narcissism to religious proportions.
I think that something derived from taoism would suit gnomes. The idea being that there spirits everywhere, you must live in harmony and balance with the natural forces/ order of things and that your attitude can affect that harmony to your net advantage or disadvantage.
For goblins instead of gods give them fables and fairy tales. Stories of how foolish, stupid, cruel or otherwise vice ridden people receive some truly horrific and disproportionate retribution in the form of an ironic punishment inflicted by gobliniods. The original moral being "don't do things like X" has become twisted into "Inflict ironic horrors on people like X; for example..." You could also say that they are driven to reenact these tales again and again.