In the ACT I think you would be bound by the Uncollected Goods Act. I expect other states have an equivalent. That lets you give notice then dispose of items, retaining the funds in a trust fund for some period, deducting a reasonable amount for costs, which might be as much as the goods are worth in some cases. I found this out when finding out what to do about a car that seemed to be abandoned but was not reported as stolen. The police and motor registry could not give me details about the last registered owner. Eventually it disappeared of its own accord and perhaps it had been owned by a local who did not respond to our newsletter item.
You might be able to do some of the things you suggest if you have a bylaw about this. In your case it is more obviously stuff left by owners and their tenants so by laws apply to them. Perhaps it is worth proposing a bylaw that would prohibit the storage of stuff on common property without permission and allowing the OC to dispose of such stuff any way it sees fit after some period and after some reasonable notice of some sort.
Do others have such a bylaw?
If it is convenient, you might deal with the current batch of stuff this way although that will leave it there for a while longer as you call a meeting, pass the resolution, register the new bylaw etc.