Can I Re-use Unfiltered Frying Oil From Night Before?
As far as food safety goes, it should be safe to refry food with it (after all, you are heating this up to ~400 F again, bacteria stands no chance)

The filtering helps on the flavor department. As food particles/breadings fall off, they burn and impart a burnt flavor. If you reuse oil with much burnt parts, the burnt flavors will come through lot quicker.

Alternate to cheesecloths: 
If you notice hardly any food particles in the bottom, you are good to go. if you have food particles, I can suggest either


Pour the oil slowly to another vessel, leaving the last half inches or so, and the food particles will remain in that last bit of oil. Discard that oil and use the remaining oil.
Use paper towel to filter.


Edit: If you want to go deeper in ther knowledge-base, heres an excellent source: http://www.seriouseats.com/2013/09/ask-the-food-lab-how-many-times-can-i-reuse-fry-oil.html