I use U2 as a medicine in three ways: to soothe, to empower, and to find meaning/elevate my soul.
The soothing part is the simplest. If I feel very raw, pretty much any of their songs make me feel calmer, more centered. While the ballads are a more obvious choice, even songs like Out of Control or Mysterious Ways can feel soothing. I can't overstate the importance of their music in my life in this regard, and even during my 15 year hiatus I'd call the music up in my head frequently.
While any of their songs can do the trick for me, my best example is Tryin' to Throw Your Arms Around the World (especially the Zoo Radio version). Its place in my life as a soothing medicine has nothing to do with the lyrics or meaning. Adam's bass line and particularly Edge's very simple guitar line have a swaying, rocking quality. Bono's voice is always soothing.
Next is the empowering medicine. The simplest version of that is just putting a little spring in my step. But some songs are explicitly empowering in their progression, melody, and lyrical meaning.
I think I will choose Stuck in a Moment as my prime example, which may surprise some. I liked this song on Leave Behind; it's catchy and has a nice melody imho. But I didn't "get" the song till I saw Bono and Edge play a gorgeous, stripped down acoustic version on Letterman. (If you haven't seen it, I highly recommend checking it out). It's a tough love song, but emphasis on the love part. I feel empowered listening to it, like when things are tough I can, well, walk on.
The most complicated medicine is spiritual, to find meaning, to elevate our souls. Sometimes it's through the music, sometimes the lyrics, sometimes both. There is a joy that goes into my heart and fills it up when I hear Edge's chimes burst through the keyboard background at the beginning of Streets (and again when Larry and Adam kick it up, and again when Bono starts singing - but it all starts on those chimes), and I know I'm not alone in that. It's more than being soothed, it's being lifted.
Sometimes it's more about the words, and those words aren't always rainbows and unicorns. Every Breaking Wave is about some hard stuff, and the vast majority is centered on defeat, but all the defeat leads to being ready to be swept off our feet. This song has a lot of meaning for me personally.
Other honorable mentions include Ultraviolet, Acrobat, Kite, the Troubles, Ordinary Love, and Little Things.