Hi, ALL spec sheets show capacitors on the input and output of the LM78 series regulators.
You need 2 caps on each of the regulator outputs, a 0.1uF ceramic and 10uF or up to 47uF electrolytic capacitors.
And they should be as close physically and electrically to the regulator IC as possible.
Also with 18Vac measure how much your unregulated DC is, you may need heat sinks on the regulators due to the voltage drop across them. Especially the 7805.
Tom..... 
ps, guys, what level of programming, electronic theory, electronic assembly do you have?