So what are the overall projected odds of Dems winning things overall? From what I've seen a house win seems likely and senate loss is also likely. If this is what happens how will this effect the balance of power? So for example if the judge nomination vote had happened with the likely outcome of this election would it have passed?
Most current models have Democrats with about an 85% chance to take the House, and Republicans about an 80% chance to hold onto the senate... I'm sure some project higher, some project lower, and of course, it's all a guessing game and it's only as good as the data, but... those are the guesses. And, again, 85% chance doesn't mean 100% chance. Nate Silver, the person who runs the political polling/analysis website FiveThirtyEight constantly reminds people this... In 2016 we made the collective mistake of assuming 65% chance meant 100% chance. It doesn't. Silver makes the analogy, in an NFL game if a team takes a 1 TD lead going into the 4th quarter, on average they have a 75% chance of winning. Nobody should look at that 75% chance and then proceed to turn off the TV as if it's a done deal, yet that's what we often do with polling and polling data. We look at a 52/48 poll and pretend it's 100/0, and then the models based on that that suggest that a poll that close will result in a 60% chance for the leader to win... we turn that into 100% in our minds.
Speaking about Kavanaugh, yeah, the senate approves Supreme Court nominees, so let's say that these numbers work out to be true, then in that case, Republicans likely still would have confirmed Kavanaugh over Democrats. Although, hypothetically, let's say that Democrats somehow beat the odds more and took more control of the House than is projected, then that could give some moderate Republicans some pause during a future confirmation hearing, they might lean more moderately on divisive, unpopular issues knowing that their seat could be threatened come the next election.
How this effects the balance of power is in a few ways, but generally, whoever controls the House of Representatives controls committees, the agenda of the legislature, and ultimately, is a check on the power of the president and legislation. It does introduce some risk in that you're likely to have more threats of government shut down, or the President Veto'ing bills instead of signing them. But, on the flipside, if you have congressional majorities you have the power to launch more investigations because you control the committees that oversee those investigations. So, for instance, you can force individuals to testify publicly in front of the American people, which can bring to light more scandals or damage them politically. This can also backfire of course (for instance, backfired on Republicans who had Hillary Clinton testify about her private email server in ~2015, and it was widely perceived as a political stunt that embarrassed some Republicans while making Clinton look more in command).
Ultimately, a Democratic House and Republican Senate will have to compromise on legislation. It would effectively put an end to attempts by Republicans to, say, gut Obamacare or put financing into building a wall. Congress also holds the purse strings on the federal budget, so it allows Democrats to prevent Republicans from cutting spending in key social programs, or designate spending for other programs. Ultimately the president has to sign legislation that passes both chambers of Congress, though he also has the power to veto any bill and send them back to the legislature (which can override his veto, but it's rare, typically veto'ed bills get reworked or abandoned). But, the public generally has a negative impression of the Veto, and so if a president Vetos too many bills then it can reflect poorly on him.
Congress' power to investigate, though, might have the largest effect, especially with Mueller set to give a report to Congress on the nature of Russian meddling in the 2016 election. If Republicans controlled the Intelligence committees that oversee that report, the report could easily be buried, not released, or spun in some way to benefit the President. With Democrats in control of the House, that is less likely.