You know, for GameFreak to deliberately screw a Pokemon is one thing, but to give it basically the same ability in the Dream World is a whole new level of idiocracy. Let's all give GameFreak a round of applause before I begin, shall we?
Delibird - The Delivery Pokemon
Well, Ice/Flying isn't all that great offensively, but there is worse. Sure you have STAB that can hit Dragon, Grass, Fighting, Ground, Flying, and Bug super-effectively, but most of these types are paired up with something to make them neutral against Delibird's STAB moves. Defensively, we have an immunity to both Toxic and regular Spikes, but a massive x4 weakness to Stealth Rock. We also carry weaknesses to Electric, Fire, Steel, and Rock type moves, which is a fair portion of moves in the NU tier with such high prevalences of Fire and Rock types.
Vital Spirit is a fairly decent ability, preventing you from falling asleep. Has an ingame effect, but nothing much else going on here.
Hustle is probably Delibird's best option for a Choice Band set, as his high-accuracy moves will get a much needed bost damage wise.
Insomnia proves that those working at GameFreak are lacking something mentally. Delibird, a fairly useless Pokemon that could use something to boost it's usefulness, already has a very similar ability in Vital Spirit. If you prefer it over Vital Spirit, go ahead and use it.
And you thought Luvdisc had mediocre stats. Delibird's whopping 330 stat total is tied with Aron, Zorua, Finneon, Luvdisc, and a few other NFE or NU fodder Pokemon. It's base 45/45/45 HP and defences mean that Stealth Rock alone is enough to basically cripple this Pokemon, Arceus forbid the opponent have a priority move to pick off Delibird. Offensively, this Pokemon gets very little blessing either, having base 55/65/75 Attack stats and Speed. Choice Band or Choice Specs. are almost a must here if you're to do any real damage to an opponent.
By level, don't even get me started. Present is a horrible move as it is. Platinum however, was a blessing to this Pokemon in serious need of one, giving it access to moves such as Seed Bomb, Signal Beam, SKy Attack, and Gunk Shot, as we all know Bayleaf needs a strong Poison move used against it in order fend it off. Avalance is the only "okay" move that came as a TM in Generation IV. It gets Ice Beam, Water Pulse, Focus Punch, Aerial Ace, and Brick Break as regular TMs. Not much to work with here. Dream World gave it Ice Shard, which gives it some usability but already had through breeding, and breeding gave it Fake Out, Ice Punch, Rapid Spin, and Aurora Beam. Still not much to work with.
My Christmas Choice (Special)
Vital Spirit / Insomnia
4 HP / 252 Sp.A / 252 Spe
-Hidden Power Electric
It's not the ideal set for the Christmas Penguin, but it's somewhat okay for the surprise factor. Ice Beam is Delibird's best STAB, and hits things like Bellossom and Butterfree, while nabbing a KO on some Ground types in NU. Water Pulse hist pesky Fire and Rock types, albeit leaving Delibird in on them usually isn't a smart idea. Signal Beam hits Absol and basically anything the previous two moves don't. The last move, Hidden Power Electric, completes the pseudo Bolt-Beam combo, basically completing the coverage. Regardless, the Special Attacking moves of Delibird are limited, and this set really has nothing going for it but the surprise factor. If Hustle works with Special Attack too, use it in place of the two other abilities, but if not, just run one of them.
Unwrapping the Gift of Choice (Physical)
Delibird@Choice Band / Choice Scarf
Jolly / Adamant Nature
4 HP / 252 Atk / 252 Spe
-Brick Break / Focus Punch
With some better attacking options, Delibird is a better Physical "sweeper" than it would be a Special "sweeper". Ice Punch and Aerial Ace are STAB moves that allow it to hit Dragon, Grass, Fighting, Ground, Flying, and Bug Types super-effectively. Seed Bomb adds to the coverage, hitting stray Water and Rock Types, while Brick Break hits Ice and Steel Types. Brick Break is a better option over Focus Punch in this case, as having been choice'd, a set-up attack such as Focus Punch isn't as reliable except against a well-predicted set-up Pokemon. Probably Delibird's best set.
Revenge Killer of the Century
If you have a weakened team, fear this Pokemon. It will end your team. Seriously. It'll come in and Use Fake Out, then abuse either Quick Attack or Ice Shard and end whatever chances that said Pokemon had of completing a sweep. Focus Punch is there for the aware player that expects a Fake Out only to take Delibird's strongest move to the face, and then get picked off by Ice Shard or Quick Attack. Purely surprise factor, but might actually be viable specificly as a Revenge-Killer. Gettin' swept by Delibird.
Rapid Spin support is a must with Delibird, as Stealth Rock is it's biggest threat. Baton Passing it a few Swords Dances and Speed Boosts from a Ninjask is a fairly decent idea. If you're looking to beat a Delibird, get help. If you need to look, quit Pokemon altogether, as so much beats Delibird without trying, it's not even funny. You could throw it on a team with a Snover, but Delibird isn't really worth the team slot. Too bad GameFreak had to drop the ball on this one.