Many answers either don't give you enough energy (oars), require advanced manufacturing (big electric engines) or both (solar).
You could go for biofuel or coal-based fuels, given that those engines run on nasty bunker fuel to start with, but this would require massive quantities of fuel, which is unlikely to be available. Keep it around as secondary propulsion, but don't rely too much on it.
Solar isn't an option (not enough energy in the first place), but wind is. Using sails on such a behemoth is going to be a challenge. And you are going to be limited in your travel direction. Still, it may be a good idea when conditions are favorable.
If you want more flexibility with wind (and go more greenpunk), use wind generators as well, especially airborne ones (assuming the tech matured enough before the apocalypse): they are lighter, can potentially reach higher-altitude winds and are easier to retract in case of storm. You can go against the wind with those, in particular.
But wait, didn't I say that big electric engines were a problem? Well, if you managed to salvage some of those pre-apocalypse ones, you could still be good. However, let's assume you couldn't. Then, go for direct mechanical transmission. Your flying wind generators don't carry big turbines. Instead, they are kites that go up and down, periodically pulling on their line, which then directly (through a gearbox) make the propeller(s) move. Don't get me wrong, that's going to be a complex, maintenance-heavy, potentially breakage-prone (plot! drama!) piece of hardware.
Note that when conditions are favorable and you don't want to wear your hardware, you can put flying sails on your kites instead.
The kites may still have small turbines for onboard electricity, and for powering the kite control surfaces (or even reversing the turbines as propellers to gain altitude). You may also want some batteries for that. If you need only electricity - say, you're at port and want to sell on the energy grid - plug them on generators (or mount turbines on them) instead: many small, fast-rotating generators are easier to make than few giant, slow-rotating ones. Which is, in fact, why you'll see small flying windgens, an possibly solar-thermal, instead of traditional giant windgens on land.
You may want to store energy for dead wind days. If you can, cram a small power-to-gas station on the ship using, say, electrolysis and Sabatier reaction to produce methane on windy days. Note that you'll have to find a way to use methane on your engines.
Now, you tell me, why not have bigger, more efficient power-to-gas stations on land and simply use them to refuel your ship as before? Because it's cool. And because you may not want to count on external infrastructure, but mostly because it's cool.