Chirp can be found at Plum Canary. It's basic function is to provide a way to let you assign tasks to people (in projects), provides a way for assignees to update same, then gives you a dashboard view of everything. (Said another way, it's core data objects are Tasks and Projects, which is what you seem to be looking for.)

You didn't really state all your requirements. But given what you *did* say, the "matches" for your needs are:
- Works offline (using a local cache of the data), then syncs changes/additions/deletions through a network-based service when you reconnect;
- Keeps all the status entries for a single task (/project) in one organized place;
- Works among team members;
- (You didn't say whether it needs to work between organizations; it does).

The "mismatch" for your requirement may be handheld access. I couldn't tell if you needed access from a mobile PDA (e.g. Treo, etc.). It doesn't have that; it's computer/laptop application only. (No web interface either). But it's available for both Win and Mac. The server is provided through a subscription service on the 'net, so there's no server to set up (which eliminates the Win/Mac/Linux debate of the above messages.)

If you can do without handheld access, IMHO this is a nice app for people who travel and manage teams / projects.

Hope this helps.