Each one contains an LED which suck down the standard 2(ish) volts, and 20mA.
What are you talking about ? (the forward voltage ? (1.3V ?)
My initial plan was to power them via the 3.3v port in parallel, but I'm looking at using 18 illuminated buttons and possibly a 16x2 LCD. So about 360mA for the buttons, and another 100 or so for the LCD screen. The LCD will be powered via the required pins (using a backpack) so am now concerned about shoving too many milliamps through the Arduino and making something go snap, crackle, pop.
Forget about using the 3.3V for leds. In fact , in your case, forget about the 3.3V until you are more familiar with arduino electrical specs. You can find them on the arduino home page.
You can power up to about 800mA from the UNO +5V , and you NEVER use 3.3V for leds. (EVER). You use 5v and a 220 ohm resistor.