The solenoid is the black plastic piece on top of the zone valve that turns the valve on or off when the controller tells it to.
It's common for all the valves to be in a single valve box somewhere near the controller.
In some installations valves may be dispersed throughout the property and I believe that's the case based on your photos.
The round valve box on the bottom appears to be used as a junction box for the control wires. Eight wire nuts indicate you have 4 zones and should therefor have 4 zone valves with solenoids.
It looks like there are 3 cables. (maybe 2, the picture is cut off) One comes from the controller and the other two (or 1) should split off to valve boxes.
The second photo of the rectangular box appears to have a single valve in it. There's too much contrast in the photo to really be certain. If you can take a picture with the contents of the box more evenly illuminated it would help. I think I see a valve body but not sure I see a solenoid and not sure what those tan components might be. I can't make out any wires either.
Best bet is from the round box on the bottom of your post, dig out the cables a little to try to determine which direction they may be going. Follow that path and you should hopefully find the other valve boxes. They may be round or rectangular.
Keep in mind that just because you have an irritrol controller does not necessarily mean you have irritrol valves.
Images from http://irritrol.com/