I totally agree on repeating the song - you want to make it your own personal earworm. My bf - the "Musician", wants to play different CDs all the time. Me, the "singer" wants to play the same song over and over (and over and over). Singing along to a cd, I start singing soft with the cd loud, and after a few run throughs I turn the cd down and me up so I can actually hear what I'm singing. Sing in the shower. In the car. Practice few songs at a time so that you nail one and move on. I find reading the lyrics helps lock it into my memory, but I don't really want to have to rely on lyrics on stage - even if I have them with me, they're only for emergencies. Like with playing, you need to know the words well enough to fake it when things go wrong (like, when the band stops playing (happened), or you skip into the wrong part of the song and need to fake your way back (happened), or the tech cuts out (happened - welcome to the unplugged show!).
I'm a bit new with the singing and playing, but so far, I find I need to get one part down (the uke) before really concentrating on the words, but I'll scat along with the song from practice one so that all parts are being learned together, which makes them easier to integrate.
I'm also big on what I call "DJing" your set. Even if you're only playing one or two songs, it's important to capture your audience, grab their attention, and bring them with you for the ride. I'm usually going to play my funnest piece first - I want them bopping (or even dancing!). Leave the ballad-y, technical stuff for later. If you can win them early, your nerves will come down just because you can FEEL that they're with you. Smile. Tell them a story. Tell them a story like they're your best friend. A song isn't just words, it's a message that is being entrusted to you for a short period of time. Make eye contact if you can. If you hear a positive comment while you're going, sing the next line directly to that person (and watch while they smile and flush). Dance in place with your uke - sway - if you openly 'feel' the music, they will too. Sing LOUD. Don't scream (unless you want too), but make your voice a presence to be reckonned with. Too many of our local open stagers fade into the background. My first word on stage is delivered in a way that will hopefully make the rather drunken bar patrons shut up for a second and listen. And practice your voice separate from your instrument - anyone can sing, just like anyone can play the ukulele, but it's in the practice that transforms a few chords and some words into a song that grabs people. My favourite tunes to practice my singing? O Holy Night (in June - and I'm not christian) and the Star Spangled Banner (and I'm Canadian). Why? Because they're HARD! Because I need to use all my breath and my openness and my power to hit all the notes. And I sing blues and folk for the most part, but it's not as much of a workout. Sing from your belly. And most of all, don't just sing like you mean it - actually mean it. The audience can tell if you're just phoning it in.
But the best thing for nerves - know your song. Know the next word, the next line, the best places to breathe, etc. That way if your brain cuts out, your mouth will keep going until it decides to come back