A lot of people have already mentioned that Oumuamua impacting the moon would not have a serious impact for us here on earth. We have some reason to believe that humans have witnessed massive lunar impacts before. There's a great story from 1178, about a few monks who believed the world was ending when they saw an explosion "split the moon in two" and caused it to sputter out "fire and hot coals." Some people believe what they really saw was the impact that left the Giordano Bruno crater!
So if you want to know what would happen if an object with a lot of momentum hit the moon, the answer is probably, "It would look really cool!"
Besides all that, I want to set the record straight on a few things, since you mentioned Oumuamua specifically. Oumuamua didn't really get all that close to the Earth. In fact, it maintained a healthy distance of at least 24,180,000 km, which is more than 60 lunar distances away. The reason there was a lot of speculation of, "Oh no, what if it had hit us!?" isn't that it got too close, it's because it was going too fast.
Part of what made Oumuamua such an extraordinary discovery is how fast it was going when it passed between the sun and Earth. On September 9th, scientists clocked its maximum velocity at 87.7 km/s. Based on that, they were able to calculate that it was moving at about 26.5 km/s when it entered our solar system.
When it entered our solar system.
No other object so close Earth has ever been confirmed to have actually come from outside our solar system. 26.5 km/s may not sound like a lot, but it's still fast enough for Oumuamua to break the sun's escape velocity. So, since it didn't crash into the moon (or anything else, yet) as it passed through our space, it should now be on its way back out of the solar system!
That's a bit of a tangent, but I think it's worth bringing up. Anyways, here's my back of the envelope guess for what would happen if Oumuamua did strike the moon, right at the perihelion of its orbit. The energy of the impact would be:
- volume = 180 × 30 × 30 m^3 (observed)
- density = 2000 kg / m^3 (blind guess)
- mass = volume × density = 3.24e8 kg
- velocity = 87.7 km/s
- kinetic energy = 1/2 × mass × velocity^2 = 1.25e18 Joules
EDIT: A previous version of this answer figured the impact would have an equivalent of 23 tons if TNT. This was way off, because I was misreading "km/s" as "km/h" when I gathered my information. The correct kinetic energy is orders of magnitude higher: 2.98 × 10^8 tons of TNT, (about 10 Tsar Bombas, and a bit less than 1 if you slow it back down to 26 km/s). Apologies for getting that very wrong!
So I'll revise again what I said earlier. It would be really cool if an Oumuamua-like object hit the moon at max speed, and probably would be the sort if thing you could see with the naked eye — just like Gervase of Canterbury allegedly did back in the 12th century.