Many reticulation solenoids operate from AC, and do so because operating them from DC can cause issues with corrosion.
Do you have any solenoids? Are they AC or DC? What current do the require?
You may have to look at using a triac to switch them.
Frankly, a relay may be easier (note that you'll still need a transistor to operate the relay, a picaxe will not be able to supply enough power to operate a relay (unless you can find a relay that required 5V 20mA or less that is suited to your needs)