Unless he wants to go for a cup, and a major contender sees a use for him, why trade Neil? He's perfectly fine as a 13th forward, apparently has leadership qualities, and seems likely to consider retirement at the end of next season considering he'll be 37.
Let him and Phillips retire as Senators at the end of their deals and just be done with it.
I wouldn't trade Greening right now. Ottawa has Mac, Michalek, Hoffman, and Greening down the left side with Legwand as an option if he plays wing instead of centre. Unless someone comes out of camp and really shows something, they don't have as much depth on the left side, especially with injuries as a possibility. Greening's value is at an all time low. They don't really need the salary space right now since there is nobody to sign. Might as well give Greening another year and see what can happen.
With Legwand potentially able to take a spot on the PK, Condra could lose his spot on the team if Lazar makes it. I have no idea what his trade value is. He is a good fourth line shut down NHLer who can play the PK. But he only has a year left on his deal. Maybe a late pick in return. Maybe package him with a pick to move up a round.
Condra is better than Neil on the ice, but Neil is probably more important to the team as a total package for what he apparently brings off the ice, and how he is perceived by long time fans. It's just not worth it to rock the boat by trading him when he potentially has 1-2 seasons left in his career and can be a 12th/13th forward.
Kassian was the 13th forward last year, so that puts some things in perspective when you consider that Kassian makes Neil look like Wayne Gretzky.