Debajo
debajo [de] normally has an object introduced by de. I think there’s pretty much always some object, which can be implicit and omitted, though.
debajo de las sábanas debajo de la cama
debajo de X=bajo X
Bajo
bajo is used without de.
bajo las sábanas bajo la cama
It is also used in abstract contexts like bajo llave, bajo inspección, bajo el nombre.
The word bajo is also an adjective, the opposite of alto, but that’s another story.)
Abajo
abajo normally implies movement (de arriba abajo; hacia abajo etc.).
According to DPD 1 , abajo is also used to mean ‘on the lower level [=floor]’ as opposed to debajo (which is purely spacial, precisely below someone/something else). RAE says 2 that it is colloquially used with prepositions instead of debajo in some regions, but they consider it incorrect.