To the question originally posted:

A "learning technique" advocated by an otherwise incompetent acquaintance many years ago was based on the assumption that you learn, and retain, things better if broken into short - sometimes very short bits. A few things I memorized at the time using his "system" (when I was about nine) are permanently and obnoxiously retained and seem incapable of fading.

You might find it helpful to pick one or two songs and repeat just one verse, or perhaps even just a single line, out loud, sung, spoken, or just silently in your head, until you're very sure that it's "permanently stuck." Then on the second day ... proceed to add another verse or the next line. Resist the temptation to "do the whole thing" until you've added on the little bits, one at a time, in proper sequence.

Quite a lot of recent "memory research" has found that memory is greatly assisted by "sleeping on it" fairly soon after the initial learning, so going over one or two songs, or even just one or two verses, within an hour or so of bedtime, may help. New stuff more than a few hours¹ before sleep seems to be less well recalled than when you get at least an hour or two of sleep within a couple of hours after rehearsing.

¹ One recent study reported a significant drop in recall with 5 to 6 hours delay before sleeping, so something less than that may be better.

Having a few songs that are "solidly embedded" quite likely will give you the chance to perform those songs with less of the nervous tension you mention experiencing, and once you build your "performance experience" a bit you'll likely find that it takes less concentration to add to your list of "well known songs." Getting the first few indelibly known may be the first step toward the performance confidence that may be your real problem of the moment.

Repetition is the key, though. One doubts that Marty Robbins has any problem remembering the words to "El Paso."

John