I'll start: some years ago, a medical professional recommended I take a daily omega-3 supplement. What I got naturally was fish oil capsules, and these of course had the nutrients I needed. So problem solved. But not only did these make me queasy, they also (I'm so sorry for this imagery for those who've never had these) gave "fish burps". Basically, after ingesting them, they can (and for me consistently did) give you these nasty, tic-like burps that taste like you let a fish decay in a bucket for three days and drank that water.
This goes on for a while until the I realize that they sell "burpless" fish oil. The day was saved, and I went home with a new lease on life. Well, until I tried it and I realized that it's not so much "burp-less" as it is "burp-lite". It just reduced the severity of the symptoms but meant I still felt slightly sick and could still have those nauseating burps. I eventually gave up on it because even just one stray burp felt that gross.
Later on, I went vegetarian (I'm now vegan), and although at that point I had plenty of ALA in my diet, I decided to look back into an omega-3 supplement as a precaution since my diet had shifted so dramatically. Of course fish was out of the question, so I looked into alternatives and landed on flaxseed oil capsules. These were more expensive per capsule, but I felt that they made up for it by having 1.6x the omega-3 per capsule. Taking one for the first time, I felt 100% normal. No upset stomach, no burps, no weird fish taste (in fact, if you crack open the capsule, the oil is quite bland). It worked flawlessly. At that time I didn't avoid the gelatin in the capsule as I would now, but you can find flaxseed oil in plant-based capsules for a slightly higher price from suppliers like Deva.
TL;DR: flaxseed oil supplements omega-3 without nasty side effects like fish oil capsules. It just works, and I wish I'd known about it so much sooner.
is it possible to add flaxseed (or some other) oil to your diet instead of taking pills?
Yes. You could also just add ground flax to foods when preparing.
Yeah, this is what I do. It's actually what I've done for decades, even before going vegan; I've always been allergic to seafood and nuts, so omegas are kinda hard for me to get.
Ground flax is great in a lot of things, morning oatmeal and soups are probably the big ones (though, does make is 'gooey', but for soups, does make ot similar to adding flour to thicken).
Whole flax seeds are better in stuff you don't want 'thickened'.
Just as a sort of PSA: You will get no omega acids from WHOLE flax seeds. You need to ground them up first! This should be done shortly before consuming as the ALA in the seeds tends to oxidize when exposed to air.