If there is no oil it is not going to work... Fill to the proper level and see how things are...
Oil can leak external or internal... if it is leaking between the trans and engine... it will be in the engine crank case...
If it's leaking externally it will be on the ground... either during operation or after you park it, depending on where the leak is... if you use external hydraulic equipment it may be leaking there...
If you are saying that the 3pt is bobbing when it should be supporting a load the 3pt cylinder is leaking, that's generally a internal leak and you will not loose any oil from that... it is just very un-handy... KennyV
PS. ... DON'T run the engine with low hydraulic oil... you will damage the pump...