Aerobatics & fluids

How do aerobatic airplanes manage fuel and oil to maintain even flows
during maneuvers?

Most fully aerobatic planes have inverted fuel and oil systems. For oil, the
Christen inverted system is pretty common, which essentially is a steel ball
that flops up and down and acts as a check valve for directing oil flow.

For fuel, the majority of systems consist of header tanks, that either have
two outputs, or fill when upright, and then feed when inverted.

This is based on my limited experience in Decathlons and Extras, but I think
similar systems are also used in Pitts and other aerobatic planes.