A lot of voltage regulators can not handle voltages higher than 30-32v. 36v is a bit high. For example, LM7815's absolute maximum rating shows 35v input voltage, but other regulators may be capable of more.
You need some input capacitance and some output capacitance on the regulator, something like a 10uF electrolytic capacitor on input (doesn't have to be exactly 10uF, but anything higher than 100uF is unlikely to make a difference) and at minimum a 0.1uF ceramic capacitor on output is recommended.
If the 12v and 9v and 5v regulators are very close to the 15v one, you'll be fine with just some 0.1-1uF ceramic capacitor on the input for these instead of the 10uF electrolytic.
Keep in mind linear regulators work by throwing out the difference between input voltage and output voltage as heat.
So for example, at 100mA (0.1A) current, the 7815 would produce (36v - 15v ) x 0.1A = 2.1 watts - usually for more than 1 watt, a heatsink is recommended.
Each of these regulators consume around 5-10mA just to work (see quiescent current in datasheets), so keep in mind that it adds up if you cascade:
7815 - 20mA (5mA for own, 15mA consumed by 7812)
7812 -15 mA (5mA for own, 10mA consumed by 7809)
7809 - 10mA (5mA for own, 5mA consumed by 7805)
7805 - 5mA for own functionality
My advice would be finding a smaller power supply somewhere in the 18v and use an adjustable regulator like LM317 or LM1085 (or others with 1085 in name, LM is used by one manufacturer, there's other prefixes)
If you use a classic transformer, I'd also suggest to use one with two secondary windings, and switch between having the windings in series (more output voltage, less current) or in parallel (lower output voltage, 2x the current) so that you'll reduce the amount of power wasted on the regulator.