For most vegetables, it is very difficult, if not impossible, to retain their quality once they have been cut. Your efforts would be much better spent either improving your cutting/chopping proficiency or in cooking entire meals ahead of time. Also, you could prepare components, such as sauteed onions or peppers, and maintain relatively high-quality versions of those.
Meat is a different story. You can do preparations in advance, and freeze individual portions for later use without degrading quality.
The best way to avoid freezer burn is to have a very cold freezer (ironically, easing the cooling settings on your freezer was having the opposite of your desired effect), and to prevent your food from coming in contact with air. You can use a freezer bag for each food item, making sure you squeeze all the air out of it first. However, if you are really serious about this, you would be well-served by investing in a vacuum sealer. Air is the big enemy here, so mechanically removing air from the system will greatly extend freezer life.
Water freezes at 0° C (or 32° F), but ethanol freezes at -114° C, so you can guess your vermouth with freeze somewhere in between those two temperatures.
Noilly Prat is 18% ABV, or 15% alcohol by weight, which means it would freeze at around -6° C to -7° C, or 19-21° F. Your freezer may or may not be tuned to be that cold, but if not, you should be able to crank it a bit and get your Noilly Prat just frozen.
That said, I would not really recommend leaving an ice cube tray full of vermouth hanging out in your freezer. You may notice that old ice tastes funny. Even though you may not notice your freezer smelling, that's partly because the cold blocks smells. Just because you don't notice them doesn't mean the odors aren't there to ruin your Noilly Prat. I would recommend leaving them for a day until just frozen (covered if you like), and then moving them to a Ziploc for long term storage.
All that said, freezing will not halt oxidation altogether, but it will help, as only the exposed surfaces areas should be able to be oxidized. Since ice cubes by design have a relatively high surface area, you may consider minimizing the exposure to oxygen by other means.
If you have a vacuum sealer, using that would be a fairly simple means to limit that exposure, but a similar effect can be done with a simple Ziploc bag, as described here (note this link is focused on using this technique for cooking, but it is translatable to your scenario). Drop your ice cubes in a bag, and then slowly lower the bag into a container of cold water (the colder the better, here, to minimize melting), leaving the seal exposed. I sometimes clip things onto the bag to weigh it down as well. Then begin closing the seal, and lower the bag further into the water as you continue sealing, so that only the unsealed portion is exposed. Finally complete the seal and you should have a reasonably low-oxygen environment to mitigate further degradation of your vermouth.
Best Answer
You will have the best results if you prep by cutting and blanching prior to freezing. This should ensure that moisture content in the veggies does less damage over time in the freezer and improve color duration. I find it helpful to freeze vegetables separately rather than as mixes as you can always grab from multiple bags, but you can't unmix mixed vegetables without more work.
The majority of vegetables for stir-fry (e.g. broccoli, peas, etc) will freeze well enough, the ones in your freezer aisle obviously freeze a bit better than others. If a vegetable has a high water content (i.e. lettuce, which I hope you aren't stir-frying with) that is more integral to its structure than the cellulose it is likelier to burst cell walls in freezing; these vegetables are better to avoid.