No, you cannot directly touch oxygen in its gaseous form. While we are constantly surrounded by and breathing oxygen, our sense of touch isn't designed to detect it. Our nerve receptors are not sensitive to the individual molecules of oxygen gas. This is similar to how we are constantly surrounded by air, which is primarily composed of nitrogen and oxygen, yet we don't "feel" it. As stated in a Reddit thread https://www.reddit.com/r/NoStupidQuestions/comments/1923014/do_we_touch_air/, "We touch air all the time. We can't stop unless we manage to get into a vacuum or to surround our skin with cling wrap." A Quora response https://www.quora.com/Why-can-t-you-touch-air clarifies, "You can touch air and air is touching you all the time except that the nerve receptors on your skin are not sensitised to it."
However, liquid oxygen is a different story. Never touch liquid oxygen, as it's extremely cold and can cause severe frostbite https://www.quora.com/What-happens-if-you-touch-liquid-oxygen. The reference warns against touching liquid oxygen or frosted parts of liquid oxygen vessels and inhaling the vapors.
The aurora borealis, while involving oxygen molecules, is essentially light emissions. You can't touch light, just as you can't touch a sunbeam https://earthscience.stackexchange.com/questions/4619/what-would-happen-to-me-if-i-touched-the-aurora.
In summary: You interact with oxygen constantly, but you cannot directly touch it in its gaseous state due to the nature of our sense of touch. Contact with liquid oxygen should be strictly avoided.
