Are there gods of runeterra? If so what are their names and domains?

Closest things that I know of are Kayle and Morgana. If the League wasn't limiting their power, they'd just oneshot the whole roster.

The closest thing the League has is the demigods Nasus and Renekton. Additionally the Archangel Kayle and Fallen Angel Morgana. Cho'gath may be a deity-like being in the Void, along with Kog'maw's "daddy." Just some theories though.

Tear of the Goddess
"He who holds the tear of a goddess holds the power of creation."
"Few are fortunate enough to come across the tears of the very goddess who created our world... but those who are lucky enough to acquire a Tear of the Goddess may take pleasure in a significant boost of mana points and mana points regeneration."

The gods no longer exist on Runeterra. Over a millenia ago, they were defeated in the First Rune War and driven away - since then, religion was in great decline until completely vanishing some centuries prior to the League's establishment.

Right now, the closest thing to religion is the sun worship of Solari and Void cults. Deities are all gone, and no one has yet ascended in their place.

I'd say Rasuk and 1Eredale are right. Gods aren't used as faction defining forces as heavily in LoL as in other games.

There are other kinds of regional beliefs though. The yordles have the Mothership that they almost worship and Ionians monks are a pretty spiritual group.

Jesse Perring.

Isn't Vilemaw believed to be the spider-god from Elise's lore?

The spider she refers to is most likely not a god, but a creature who serves the Shadow Isle Kings will.

Think of Elise as a recruiter, who lures "followers" to the Isles to be eaten, which in turn creates spirits or souls (w/e) for Yorick to promote through the levels of undeath, which in turn join Mordekaisers/Hecarims army, or are forced to sing for Karthus' ult (lul).

However, the little information we know about the Shadow Isle's King speaks about his control over the realm of the dead, which chalks him up to godlike.

A couple of gods have been mentioned, Such as the Solar deity that Leona and the Solari worship or the Lunar deity that Diana follows. There's also the spider god of Elise's lore, though considering her cult was just a way to get people to feed to her giant spider thing, the spider god is also probably just a deception.