I've helped 3/5 citizens to become thane of Windhelm (finished blood on the ice, donated coin, beat the guy in candlehearth hall). I can't seem to find any other odd jobs to do around the city though. I've retrieved the white phial and killed the thalmor assassin, but it didn't count either of those.

You can try:

Adonato Leotelli in Candlehearth Hall for a delivery mission.
Torbjorn Shatter-Shield to get a "find a rare item" mission.
Oengul War-Anvil wants an item found (from a cave).

Visit 'Sadris Used Wares' in the grey quarter

I don't think they all have to be in Windhelm proper - the idea is to be "known" throughout the hold by the people of Eastmarch. With that in mind, I'm pretty sure that just picking crops for the people who run the farms just up the road from the stables counts. There are at least two farms there where you can help out. Just go there when they are outside working, harvest some wheat (I think that's about all that grows there) and sell it back to them. Harvesting crops always works for me, I usually do it just out of habit when I pass a farm and then if and when I get to the point of becoming Thane I've already got at least a couple points in my favor.

The East Empire Company could use your help.

The Argonians at the Argonian Assemblage wants you to beat up a guy.

and you could just give money yo beggers or give a drunk a mead.

Help the dunmer at the general store. Also it counts for the whole hold, and not just Windhelm