I'm trying to replace some older (late-1980s?) Leviton incandescent-only dimmers with new Lutron LED-compatible ones. There are three of them in a 4-gang box (the 4th switch seen in the pics is on a different circuit that controls a stairway light and was already replaced). Each dimmer switch controls a pair of recessed ceiling lights. The two switches on the outside (left and right--see pics) are single-pole and each control one pair of lights. The center is a 3-way that controls another pair of lights that are also controlled by a toggle switch on an opposite wall (also already replaced). The older Leviton single-poles have only two black wires while the 3-way has two black and one red wire (all hardwired--no screw mounts). I'm using new Lutron Skylark C-L 3-ways (with 1 black wire, 1 red, 1 red/white, 1 green) for all three (I can just cap the unneeded red/white wire provided for traveler on the new Lutrons per instructions in the packaging).
I've drawn a diagram to show the present wiring config. I'm guessing that the hot is coming from the black in Romex-2, which goes back to the lights (load) via black into Romex-1/3/4 (or, in the case of Switch 2 [Sw2], possibly via the Romex red in Romex-3?). All whites from Romex are gathered to one wire nut. For Sw-1/3 I'm thinking I can cap the unneeded red/white on the Lutrons and use either the black or red interchangeably to replace the older two-black config on the Levitons. I'm puzzled about how to wire Sw2 since it's a 3-way. Also, the bare grounds from the Romex are all pigtailed and screwed into the box. The old switches don't have ground wires, but the new switches do include a green ground. Do those have to be connected too, or can they be ignored (or gathered together and capped?) since, I assume, the circuit is presently already grounded.
I'm pretty much a noob with all of this and have tried to describe it as accurately as possible using what I hope is proper lingo from what I've garnered through research trying to understand all of this. Any and all help would be much appreciated. Many thanks in advance.