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There needs to be a cease fire and a deescalation. Unfortunately parties on both sides are invested in it continuing.
The UN can't really do much... the vast majority of resolutions are not legally binding in the first place.
It's basically just a place for people to talk, with zero actual power. >

The UN itself can’t do too much because Russia is on the security council. That said since WWII there has generally been a global consensus on a rules based world order and these values were enshrined in the principles laid out in the UN Charter. A war of conquest in the late 1800s or early 1900s would not have caused much of an international response but a clear violation of the principles of the UN Charter and a threat to the rules based internationally order has triggered a great deal of support for Ukraine. Dozens of countries are sending them weapons and even Russia’s closest allies aren’t joining in in the invasion. Hell Kazakhstan won’t even recognize the illegal annexations and China is refusing to send lethal aid to Russia. 
The UN itself isn’t going to stop Russia but rather countries acting in support of the values of the UN are actively preventing the Russian invasion from succeeding. >

love the metaphor >

The UN is its member states. They meet in its General Assembly and vote on shit. They could vote to remove Russia's permanent seat on the UN Security Council which allows it to veto resolutions that on matters of international security. 
I would expect them to do that if Russia used a nuke in Ukraine. But it is (ahem) the nuclear option. If they do it, they risk destabilising the UN (others, like India, would demand to take Russia's place, and a new argument would start. (I think they should do it, but this helps explain why they might be reluctant. ) >

That may be the only reason they would do it. The entire point of the permanent seats on the Security Council is to keep the five biggest nuclear powers happy and prevent any civilization-ending nuclear wars between them. If you think of the of the Security Council as having the first goal of "prevent the world from ending in nuclear war", with all other goals being a distant second, then the Security Council has actually done a decent job so far. >

The UN and international law is playing next to zero part in any decisions in this war. It’s simply raw military power. That’s the only factor. USA would be happy to destroy Russia with or without the UN if Russia didn’t have civilization ending nukes. Other countries feel the same way. Either they don’t have the military strength to do anything so they won’t. Or they do have the strength but don’t want to risk the war. 
The military concept of escalation dominance applies to this war. If USA shoots down Russian planes, the Russians will reply with an escalation. The Americans will respond in kind. This will escalate to nuclear war and the death of humanity. This it what keeps America from intervening directly. >

Literally nothing since Russia is a permanent member of the security council which can veto any decisions >

UN can't do much vs Russia, let alone join the war. That would mean every UN country would make themselves a target, especially the ones who actually do damage against the russian troops. That is why probably NATO doesn't help Ukraine with military troops. In case someone did helped Ukraine with military troops, if they are NATO member, the art. 5 would not activate and i doubt anyone would be ok to being nuked. >

Theoretically, it could declare the invasion illegal and put together an international peacekeeping force to remove Russian forces from Ukraine's sovereign territory.
Practically, it won't do anything for a number of reasons. Russia is a nuclear power. Russia is a permanent member of the Security Council with a veto. Russia has multiple allies that would work to undermine and block such a resolution. Russia's naked display of aggression works in part because they knew that the consequences would be like limited for these and other reasons. When it comes down to it, international law is set by the consequences a state faces for engaging in certain acts. Merely by engaging in the invasion Russia has changed international law, just the same as how the United States did when it invaded Iraq two decades ago. >

Not much. The UN mostly just functions as a forum and has few real powers. I suppose Russia could be suspended from the UN security council, but even in that case there is no precedent for it and likely no framework in the charter. Even if there was it would probably require a unanimous vote of the other members and that probably isn't going to happen with China or India. >

Their seat is granted by the Charter itself, and changes to the charter can only be made with the unanimous approval of the Security Council. >

Is it “Russia” or the “Soviet Union” that has a chartered seat? >

The USSR. However, the General Assembly accepted the status of the RF as the successor to the USSR in 1990. Changing that would require a change to a number of other things, all of which Russia (as a SC member) has veto power over. >

I'm pretty sure Russia has a permanent seat in the security council, so any motions other UN nations take against Russia that need to be voted on would be vetoed by Russia itself. Individual nations are left to choose if they would like to join in or not in the war. Like someone else said in a comment, smaller nations may not be willing to join the fight because of their vulnerability- which means regardless of if the security council could vote on actions to take against Russia, nations would have to basically volunteer themselves to be targets (which most won't do). >

Their vote in the General Assembly doesn’t matter, as removing them from the Security Council requires a change to the UN Charter, something all of the permanent 5 have the ability to veto. >

Some relief agencies could be directed to give humanitarian aid, but that’s pretty much it. This is just one more example of the security council vetos making the institution useless. >

Yeah this situation is exactly why one needs military alliances as a step below the UN. I'm not so far to say the UN is useless. It does have its uses, just not here. Most of the really useful stuff is really boring mundane things. The one I'm most familiar with is aviation standards through ICAO and basically the UN is the reason international aviation works. But boring bureaucracy isn't sexy and nobody cares.
But honestly the whole idea of a permanent member of the security council deciding expansion by conquest is acceptable could derail the whole organization and world order more generally. And for as much as I support the Ukrainians specifically, that's why this war is so much more important than just what happens there. >

We don't want peace we want weapon sales and exclusion of Russian oil from international markets. >

Oh believe me if you sent Republican politicians to Ukraine to help fight off Putin, there would be an agreement reached in a nanosecond.
The Republican party works very closely with thugs, erm international crime lords, like Putin. >

If you sent in Americans, regardless of political party, it may kick off nuclear war. No need for the rest of your comment. >

They could Tell them that becoming a member of NATO was always unacceptable, and never will be. Plus THEY could demand that the Ukraine begins to negotiate towards a peaceful resolution. >

I’m trying to remember their response to previous illegal invasions by members of the Security Council, and i don’t think it was much. >

One thing it can be useful for is to take the vital notes and collect evidence that can be used in the decades to come and be an arbiter of truth in the future, and leap collect evidence that leads to convictions either in a specialty court or national courts. 
This war will be remembered for centuries if not millennia. They will benefit from the extensive record keeping we do now and from an organization designed to limit bias.