[SalesForce] Insufficient Privilege when editing a Task related to an object

Imagine you have two users. Both are in the same profile, which allows them to Create, Edit object XYZ. But these two users are in different parts of the role hierarchy.

If User A Creates an XYZ, can user B edit it? The answer is only if the record is shared with him. If the Org Wide Default is Private then he will not even be able to see the record that User A has created (unless it is explicitly shared with him). He can still create his own XYZ records, and edit those. Likewise if the Org Wide Default is public read only, User B could see it, but not edit it despite what his profile allows. He can edit only his own records or those shared with him.

Sharing also works up the role hierarchy. So User A's boss can see the XYZ record that User A created. If his profile allows, he can edit it, but his profile may not.

You can think of the profile as "What can a user do with the XYZ object" and the sharing as "Which particular XYZ records can he or she do it with"

Does this help clarify?

EDIT--- Answering your additional questions

1. If OWD is Public Read / Write but the profile does not have access to Read or to Edit then you cannot Read or Edit.

2. If OWD is Public Read / Write on object XYZ and profile has Read permission but not Edit, then the user with that profile can only Read XYZ (all of them)

3. If a user doesn't even have Read access to object XYZ then they cannot see any object XYZ regardless of the Org Wide Default.

4. Not correct - the owner who is higher on the role hierarchy has sharing access to all the XYZ that his subordinates own. However, if the higher user has a profile which doesn't include read or edit then he cannot read or edit those records.

Profile Permission means do you have the ability to read or edit(OBJECT BASIS), Can I edit account?

OWD means do you have access to that record or not(RECORD By RECORD BASIS). Do I have access to edit this specific account record?

So coming to your question. OWD is Read Only. So you have Minimum Read Access to that.

Even if your profile has edit permission, as you don't have edit access to that record you wont be able to edit.

Profile(It means Permissions) OWD or Sharing(Do you have access to that record)

Ofc, OWD is most restrictive permission, You can open up your access using Sharing Rules, Territories,Apex Sharing/Manual Sharing.

NOTE: If your profile has View ALL or EDIT ALL permission than no matter what OWD is you will be able to access any records.