Erik and WonderWoman already answered clearly, but omitted one thing:
Yes, you are still under contract and all the obligations of your working contract are still in place, including that they give you tasks to do.
However, it is professional to consider the fact that you are leaving. If you estimate that a task will not be completed by the time you leave, or requires investments into you that the employer will not recover (e.g. learning a new skill), it would be right to point this out to them. Not as a reason to refuse, but as something to consider.
Another thing to consider is tasks that involve clients. If a task requires you to establish contact with a client who doesn't already know you, it can reflect poorly on the company if the next time someone else calls. It might be better for the company to have whoever will be doing the job after you contact them instead.
All of these things are theirs to decide, but some of them are easier to see for you, and thus you should point them out. The idea is to be cooperative and helpful and leave in a positive way. You never know when a positive recommendation from this company might help your career in the future.