"Which Needs Will Be Met in Free Agency or By Trade?"
The key word for me is "met." While I think you meant "addressed," I stuck with the more literal response. FB is the only "need" likely to be "met" through acquisition of a veteran. I'll respond to each position individually for you.
OG - Re-signing Hochstein would be the first step in "addressing" the "need." That would give NE Russ, Logan, Stephen, Billy, Dan C., and Ryan as OGs under contract for 2009. As many have noted, Stephen Neal is over 30 and has lost a big chunk of time to injury in his career - OG is often volleyed about as a Day One selection to develop a top talent behind Neal. Neal is not the only OG who loses time to injury, further, the performance over the past two seasons by Hochstein and Yates as Neal's primary reserves has me more concerned with the drop-off when Neal goes out (if Mankins ever goes down there would be an ever larger drop-off). As I see it, the draft is the best avenue to "meet" the need for improved play at reserve OG. I have to wonder if Russ' increased playing time late in the season at FB and TE was also part of BB showcasing his old faithful for teams who might want an OG in free agency - rather than re-sign him, NE could be looking at Dan Connelly as his replacement and be looking at Day Two or UDFA OLs as a means of retooling at OG.
OT - The real "need" at OT isn't in the top 3-4 positions (no matter how many people squawk about Kaczur or Light as losers), it's in having enough quality at camp fodder to develop the team in Training Camp, and to have good enough players to step in if one of the top four OTs are lost to PUP or for the season. NE went the veteran way to build depth at OT last season, epic fail - though waivers was a bigger success than we could have hoped.
WR - The "need" isn't for a 2009 #3 WR, it's for a 2011 #1 WR. This is a draft challenge.
TE - Again the need isn't for an upgrade so much as it's for 2010 and beyond.
FB - Not an urgent need, the most effective way to meet the need is to re-sign Evans for his leadership, versatility, and Special Teams play.
S - NE can address this need fastest by re-signing Sanders, but the draft is a means of building some quality depth at the position.
CB - Wilhite, Richardson, and Wheatley all showed enough talent to encourage the more analytical fans. The more panicy fans will pin their hopes on NE scoring big in Free Agency or with a trade, rather unlikely. The anticipated Lewis Sanders re-signing brings in a veteran presence to backstop Hobbs and the kids, this may be actually be a year where the Pats draft needs and the pool of high end CBs actually work to allow NE to invest in a round one kid to team with Wheatley and Wilhite long term.
OLB - The kids on roster are better than the available Free Agents when cost and upside are factored in. Draft a Sintim or Cushing if you want a rookie who can take OLB reps.
ILB - This is a difficult area to predict, the draft looks stronger than Free Agency, but Caserio is more likely to have a pool of someone else's reserves in mind for signing as budget conscious Free Agents who could blossom in the Belichick system.
DE - Re-signing Wright would be the most likely way to address this "need" in Free Agency. The draft, weak as it is in 3-4 DL prospects, is still a better opportunity to "meet" the need.
