Yes it is possible, but the way you have to do this depends on the answer to the following question (which is not clear in your message): Do you want employees to see their own tasks by default and still be able to see others' tasks [1], or do you want them to exclusively see their own tasks without the possibility of seeing the others' [2]?

If [1], then they can filter the tasks with their name as the responsible and save this filter as their default filter (in advanced search). Every time they will open the view, they will have their own filter showing their own task, and they will be able to remove this filter if they want to see all tasks.
If [2], you will have to create a record rule for all the users of a particular group for them to only see their own tasks. You can even set up OpenERP so that they can still create tasks for others, but once they save them, it disappears from their view because they are not the responsible.

Regarding managers, you can use the same mechanisms described in [1] and [2] to achieve that.