Right off the top, I'll just say I don't know the Sharks team all that well. To be perfectly honest, if it's not the Oilers I'm not nearly as familiar with it/him/them as a true Canadian hockey geek should be - but I'll give it my best shot. First off, Oilers - Sharks, then I'll muddle my way through the rest.
(Grumble, quick edit: I lied. I won't muddle my way through the rest at all, not now anyway. But I'll predict Ottawa in 6, for much the same reasons that I'm going to predict the Oilers over the Sharks.)
I'll talk a bit about primary vs secondary scoring as well. Another weblogger - sorry, forget who - wondered what the difference between primary and secondary scoring was. I should have thought it was obvious, but I since I don't read the weblogs of people I don't respect, maybe it's a good question after all. I'll blatantly accept the existence of such a division as a given, and talk about it in more detail in another post.

I think the key to the series won't be shutting down the primary scoring for the Sharks. A genuinely great offensive talent like Joe Thornton doesn't lend himself well to being shut down. Rather, the name of the game should be containing them. They're going to damage you, no question - just don't let them damage you too much. I didn't watch the games, but it would appear that Nashville didn't do a stellar job at this: Thornton didn't score, but did get 4 assists, and Cheechoo had 2-2-4. I hesitate to put Marleau in the primary scoring category: he was over a point a game this season, but he's been muddling along at a little over 0.5 for most of his career, although at 20+ goals a season since 2000-01 it's hard to tell. I don't have his ES/PP breakdowns handy, but I'd bet he gets a lot of power play points. So I'll call him a secondary threat, although he ranks high. This year's playoffs back me up a bit: 7-1-8 for Marleau, with 4 of those goals on the PP.
The key, I believe, will be shutting down that secondary scoring, Marleau especially. Contain Thornton and Cheechoo as much as possible, but shut down Marleau. The corollary will be avoiding the penalty box, but in the playoffs that's almost a given anyway. From the looks of it, it's Preissing and Ehrhoff feeding Marleau on the PP. (Does Marleau play the half boards and/or down low on the PP, with the shot coming from the point?)
Did this post add any value to "the blogosphere" whatsoever? Doubt it. Too bad, I'm going to continue for a bit longer.
What else does Edmonton have to do to win? Having said that the Oilers need to avoid the penalty box, we all know they can't. Even the mighty Orbs took 4PIM in G6 against Detroit. (2 were righteous, 2 were of the "Two minutes for checking a Wing" variety.) So Roloson needs to stay on his game. You can have the best checking forwards in the world, you can have Chris Pronger on the blueline, but if your goalie can't stop a beachball you'll lose the special teams game every time. Edmonton's secondary scoring needs to stay woken up - Hemsky and Samsonov came alive in game 6. Hopefully the break doesn't allow them to fall back into their poor play without the puck.
So, point form, all the things I feel the Oilers need to do to win the series:
* contain Thornton and Cheechoo
* shut down secondary scoring, particularly Marleau and the dmen on the power play
* stay off the PK as much as possible
* keep their own secondary scoring going
Key players for the Oilers will have to be, in order:
* Dwayne Roloson - can't ever win in the playoffs with poor goaltending, and the Sharks goalie situation seems a bit better than that of the Wings.
* Michael Peca - assuming MacTavish agrees with me, can he contain Thornton? maybe, maybe not. If not, I bet he can shut down Marleau. Another key PK guy.
* The second forward line: Stoll, Samsonov, Hemsky[1], especially Hemsky.
OK, I think I've said enough. My prediction: Oilers in 5. The Sharks should be vulnerable to tight checking and disciplined play from a team that can throw any one of 3 lines out without much fear, and can roll 4 effectively. Their top two lines are all capable of approaching a point a game. Edmonton are deep as hell up front now, although they're a tad weak up the middle with Rem Murray drawing in regularly. Their top 4 defencemen are as good as any team left standing, and MAB's got game - he just needs to find it. I think with Tarnstrom, what you see is what you get, but with some protection he's good enough to get the job done - and if not, Ulanov can step into the same role. Roloson's proven, also, that he's as good as or better than any goalie left.
[0] In testament to my lack of knowledge of the workings of other teams, I had to go look up and guess via icetime who plays LW to Thornton and Cheechoo. Boo me. nhl.com lists only 3 LWs playing for the Sharks in the playoffs. Guess a centre is playing on the wing, cos they've got Marleau, Thornton, Smith, Goc, Rissmiller, McCauley, and Stevenson all having played at least a game. Only three RWs too.
[1] I almost said it's a good thing that their names don't spell some sort of acronym. I hate those cutesy names. But the geek in me sees SSH there. Sigh. Since I've gone down that road... JS, SS, AH. Hey, they could be the ASS line, as in they'll make ASSes out of you if you give them room. More boo on me.