The problem with bottles
Oil paint doesn't really "dry", it hardens through a chemical reaction that turns the oil in the paint into a kind of plastic. The oil reacts with oxygen in the air and polymerizes.
If the paint is stored in a container with no air (like a squeezable tube), it can't start the hardening process until it's dispensed and exposed to air. If it's stored in a jar or bottle that isn't filled right to the top, the container will contain some air, and the oxygen will react with the paint. There may not be enough air for all the paint to harden initially, but it will harden as a cumulative process. The surface can skin over (which would need to be removed and discarded), and some of the paint below that could become partially polymerized, which will change its characteristics.
Every time you open the container, you exchange the air inside with fresh air, and more oxygen to react with the paint. Even if you open the container only briefly to take out some paint for use, you leave the container with fresh oxygen when you reseal it, which will react with the paint while it's in storage.
A container of just linseed oil can eventually do the same thing, but it's less susceptible. Without the paint pigment, the oil is better able to mix when you handle the container, so it has more tendency to become slightly polymerized throughout instead of the surface hardening.
Solutions
I can think of a few kinds of "adjustable" containers that would allow you to store the paint without air pockets:
Empty plastic lotion tubes designed for people who make their own cosmetics or want to repackage lotions for travel size. They're widely available (Google "empty lotion tubes").
Large plastic syringes (no needle, just a fairly large "nozzle"). It's easy to plug the nozzle hole to seal it when not in use. These are available on Amazon and other retailers. They're typically made of polyethylene and can be cleaned and reused, and 100 ml is a standard size.
Small, very heavy-duty resealable plastic bags/pouches that open on the narrow end. You can buy squeezable plastic pouches that are long zip-lock tubes designed to fill with juice and freeze to make popsicles, like these.
They also sell refillable plastic "flask" pouches with a capped nozzle designed to hold and drink beverages like this. These tend to be bigger than your paint quantities, but you just squeeze out any air. Or keep the empty portion flattened as you fill the pouch so all the paint is at the open end and there is no air in the unfilled portion of the pouch.
Very heavy-duty plastic bags plus an accessory resealable dispenser cap. You can find these caps at places like Amazon or at big grocery stores in the gadget section. They are typically a spout with a snap-close lid plus a clamp that seals the bag around the spout. When you use up the contents, you can clean and reuse the cap. They go by various terms, but "plastic bag spout" as a search term brought up a bunch of examples on Amazon.
You can also make your own. Cut the top off a plastic bottle that has a cap and neck with deep, continuous threads (more likely to find on a juice bottle than a soda or water bottle). Unscrew the cap and feed the opening of a very heavy-duty plastic bag through the bottle neck from the bottle side. Fold it over the threads of the neck. Then screw the cap on over the bag.
A variation is to use the top of a plastic bottle that has a flip-top cap or other closure mechanism (like a bottle from shampoo or liquid dish detergent). The bottle should have some kind of indentation between the threaded neck and the rest of the bottle (so you can secure the bag without it pulling off). Wrap the opening of a very heavy-duty plastic bag around the indentation and use a zip tie to make a tight seal. Then you can use the cap's built-in dispenser.
Use a bag similar to an icing piping bag that is completely air tight (not rolled from a sheet), and that has a good sealing clip on the back and a nozzle with a sealable cap.
If you don't want to go that route and want to stick with a bottle or jar that will contain an air space, you can slow down paint hardening by displacing the air so there is no oxygen in the sealed container. Before you recap the container, squirt in a burst of "canned air" from a duster (like "Dust-Off"). The gas is propellant and an "inert" gas. Aim the nozzle at the wall of the container so the gas creates a vortex. Then immediately cap the container. This will displace most of the room air.
Another way to do this if you have access to dry ice is to drop a few very small chips of dry ice on top of the paint and lay the lid on loosely. Give the dry ice a few minutes to sublimate and displace the air, then tighten the lid. Use just a few small chips of dry ice so you don't freeze the paint. They will mostly float on a layer of carbon dioxide and sublimate quickly, and it doesn't take much to produce enough carbon dioxide to fill the top of the container.
