Well, Dalinar, Lift and Renarin are some canon examples of weird, though they don't fit your criteria exactly, with a dead god's shadow, a boon & a bane, and a corrupted spren.
Illumination seems to be a weird Surge with a Spiritual aspect, a proclivity for a very hyperspecialized use as illusions as Lightweaving but being in essence the manipulation of waveforms. Same with Adhesion, as a Spiritual aspect melding with Gravitation for the leading, protective Windrunners and acting as Connection for Bondsmiths, used for bindings, but the method of binding in the Physical means certain physics hacks making it the Surge of pressure and vacuum. All Surges will turn out to be weird soon enough.
But for specific weirdness, I've always wondered if one could use Abrasion on things other than oneself. Keep in mind, I think that Lift has only been using this Surge in one direction: to reduce friction, rather than increase it, which given the Surge's name and the Shard whose system it belongs to, as friction can be used for binding things, I think is quite possible. I also think she could use it on other surfaces, like the Lashings and voilà ! Fire. Of course, in this case I'm specifically thinking of Dustbringers' use of Abrasion, alongside Division, which is stated to be the severence of molecular bonds. There's a lot of chemical explosion potential here, I like it.
Oh, and I've changed camp about the possibility of aging via Progression. Why? Because recently I started thinking about Lift's Boon, which was about her age, so maybe her wish wasn't granted as obliquely (still indirectly but not so far as to theorize about her phrasing of it "herself not changing..."). So she got access to the Surge which could age or de-age by being granted a Nahel Bond - tinfoil, I know but it's what made me reconsider.
Healing, or Regrowth is an aspect of the Surge of Progression. I didn't consider aging via Progression a possibility because of how most healing in the Cosmere is supposed to work: by checking your Spiritual Identity and applying this ideal state onto your Physical self. Renarin's healing of Adolin seemed to showcase this to some aspect, but that might just be because the Surges are used a bit differently between the Orders. There should be some component in the Spiritual Realm which also measures growth and decay, i.e. aging. I think it's possible.