If we're going by legends and the accepted belief here that Star Wars would wipe the floor with the Trekverse, then I see Vader simply building his own empire out here.
As others have said, why would he want to go home to Palpatine? Vader isn't incompetent politically, and he doesn't buy into all of the racist stuff about aliens, or indeed much of the Imperial propaganda in general. He sees it for what it is: something to sell the masses to earn loyalty. With this in mind, he would act how his intuition and strategic sense tells him to, not how a random Imperial moff or admiral might. Just had to get that out of the way.
Star Destroyers, of which there are four in Death Squadron, carry six years worth of consumables. Also listed in the Imperial Sourcebook is 36,00 metric tons of cargo space. It is common practice in WEG books to list cargo space as space available when fully stocked with consumables. So there is plenty of overflow for whatever cargo the Empire thinks it should steal. Enough, in fact, to steal the entire 1945 Enterprise. Per Destroyer.
The Executor also has six years of consumables carried aboard, which, when you look at the disparity in crew sizes, is a hell of a lot more than a Star Destroyer carries. It also has 250,000 metric tons of extra space. It carries more than 250,00 crew, 38,000 stormtroopers, and an entire Imperial Army corps.
The point of all this is to show just how massive the Empire was. These ships were tasked to go into space, find some rebels, kill them, and keep doing so for half a decade. With this in mind, I find it doubtful that anything would prevent them from quickly building up some form of supply network. Rudimentary when compared to the Empire? Certainly. Enough to keep them fighting until they could capture some Federation factories? Even more so.
Plus, any ship encountered could easily be captured (250 ion cannons on the Executor) and recycled, its crew enslaved, its food stocks reappropriated.
After the first few battles, no Imperial would ever have to work a farm again. Slave labor would handle it. I'm not too familiar with Star Trek (I watched Into Darkness and the one before it), but it sounds like there is a sentient species in the vicinity of the arrival zone. They wouldn't last a year.
In fact, this gives me a great idea. With their massive cargo capacity and total impunity to Star Trek weapons, I can see Vader simply cruising from planet to planet, stopping long enough to enslave the local population and work them to death mining and manufacturing while Probe Droids map a route to the next target. Anything that can't be stolen would be destroyed. Naturally, this is only effective in the short term. Eventually, Vader would settle down and turn to empire building, most likely after he'd mapped out a sufficient portion of the galaxy. But still, it's fun to imagine Death Squadron like a swarm of locusts destroying everything in the Milky Way.
If you don't know your rights, you don't have any.