The way to think about it is in terms of the receptors. If you denervate, the receptors are not going to be activated as much under normal conditions (no neurotransmitter binding, only hormonal stimulation). If the receptors are not activated, they become more sensitive to stimulus (has to do with a lot of signal transduction cascades - phosphorylation state, how easy it activates secondary messengers, how secondary messenger are degraded, and how quickly the receptor is deactivated) and also there may be production of more receptors (transcriptional compensation). So if the receptors are hypersensitive and you give an agonist drug, there will be a hypersensitive (enhanced) response.
Yup. Absence of agonist makes it more sensitive. Excess of agonist makes it less sensitive. Body just tries to compensate for all the stuff that gets thrown at it. Gotta love homeostasis.