According to the rich Hill chart the rams pick is worth 190 and the giants 2 is 162 and the 95 pick (they have NE's 3rd) is worth 40. However, there is value in having a 1st round pick so teams overpay about a 5 or 6 rounder to get into the first (10 or so points). That is a quote from Hill. So the rams could probably get the 37 and 95th for the 31 or for the 31 and 203 (rams' 6). If we want to own the end of the 3rd round, we then flip 37 to Carolina for 47 and 100. Then flip 47 and 169 (the rams' 5) to NE for 56 and 101. This would mean the rams would turn the 31, 169, and 203 into 56, 95, 100, and 101. Add in the rams already having the 94 and 99 picks and the rams would have five of the last nine picks on Day 2. With 6 day two picks, they could fill IDL, Edge, S, 2 OL, and then IDL/RB/CB/LB. Day 3 only has a 4 and a 7 but they would have already had their draft the day before.
The comments below are based off of the CBS Sportsline 7 round mock from Apr 17.
Here is who is available at 56 (rankings are from Deadpool) 34 Wilson LB, 35 Irv Smith TE, 38 Omenihu IDL, 39 Rapp S.
Now jump to the end of the 3rd, #62 Deiter OT, the guards from Oklahoma 66 Samia and 75 Powers, 74 Willis DT, 85 Wren DE, 92 Davis IOL, 93 Blair S, 94 Bonogu Edge, 97 Dean CB, 98 Smith ILB, 101 Henderson RB
So if they go Rapp then they fill 2 OL in the third, 2 DL Willis, Bonogu, Wren and Dean or Henderson.
If they gran Omenihu in the 2nd, still get 2 OL in the third, another DL/Edge, and then 2 of Blair, Dean, Smith and Henderson.