Trying to keep the explanation simple as to what U2 does but it's not easy.
U2 is used to select one of the 15 momentary solenoids. Due to how it is implemented, U2 can select only one momentary solenoid at a time. These 15 momentary solenoids are controlled by transistors are within U1, 3 and 4: Seven transistors within U1, Seven transistors within U3 and one transistor within U4.
Of the seven transistors within U4 -- one is controlled by U2 as a momentary solenoid control, four of the transistors are used are controlled by the "Continuous Solenoid Data" lines from the CPU board and 2 of the transistors within U4 are not used.
The 74154 decoder (U2) is not able to switch enough current to the final output transistors. So the CA3081s and their respective 120 ohm resistors provide additional current to the final output transistor -- the SE9302s.
Actually, the 120 ohm transistors provide the required current to turn on the output transistors, the CA3081 is responsible for turning the power 'off' to the output transistors.
Also note that Bally has drawn the output transistors (SE9302s) improperly. These are actually "Darlington Pair" transistors which means each of those SE9302s has two tightly coupled transistors internally. So each solenoid output is actually controlled by -three- transistors. One within the CA3081 and a pair of transistors in each of the final output transistors. Had to throw that in there to add to the confusion factor. Shown below is a 'Darlington Pair" transistor.Darlington (resized).jpg