Within Teamwork, you can do advanced search queries using boolean operators such as AND/OR, brackets and quotes around strings to match phrases.
You can also search for all items (of all types) with a particular tag by using #tagname in the search field.
If you know the ID of a project, task or other item in your site (you can see the task ID in the column on the left of the task details screen, and you can see the ID of other items in the URL for the individual item page) then you can enter the ID in the search field to see a link straight to that item.
You can also refine your search to a particular item type prior to searching. Select the relevant item type from the dropdown then enter your search term. The results will only show matches for that item type.
For more information, see: Using the Teamwork Search Bar