Within the profile settings, under object settings, then object permissions - I do not see the option to set a profiles object permissions for Tasks, Events, Notes, Users to no access. Appears that I am able to set the field level permissions, though it's unclear why there is not the option to set the object permissions to no access, if there's another place to do this, and if not, if removing access via the fields will have the same results. How to set object permissions to no access for: Tasks, Events, Notes, Users?
Update: In retrospect, might be worth stating the problem that resulted in this question. I am creating a barebones user and have removed links to Tasks, Events, Notes, and Users - but these object are still showing up in searchable fields by objects dropdown for the sidebar search. As I've removed object permissions from other objects, they've been removed from the dropdown, so I believe removing permissions for these objects will have the same results.