I disagree, I think some interesting things CAN be done with Dodrio and the other Normal/Flying, the only type I would declare useless is Flying/Ice without Magic Guard, however, I don't think Tery's got the right idea, though he does offer a few interesting bits. For example, the main problem with Normal/Flying is steel types. Giving them Outrage, a move many steels are already able to switch into is yet another reason for a steel type to switch into Dodrio. Being forced to switch isn't something we want to do.
One option for Dodrio is to give him a combo that would undoubtbly be the 2nd gayest legal combo in the game, second only to Machamp with No Guard and Dynamic Punch. Serene Grace and Tri Attack, with Dodrio being a powerful special sweeper. This helps it in a few ways. Most steels dislike special attacks, however, how would a steel type feel about switching into a special attacker that could freeze/burn/prlz them? Not a pretty option. sure, they might not mind prlz so much, but god forbid freeze or burn. I'll admit, Dodrio is anything but serene, perhaps some sense could be made of it reguarding the three heads.
On top of this, another way to make Pokemon fear switch ins would be to grant it Adaptability. A STAB Tri-beam is a pretty deadily force, even in a world full of ghost, as we have created several SmashCAPs full of ghost, and with Rotom figures, Gengar, Sabyleye, and Dusclops running around, its not an unstoppable force by any means, especially considering the large number of types that resist it. Adaptability makes aesthic sense thanks to its three heads providing the power to come up with the times 2 on STAB, while on his Ice/Fire/Lighting special moves he would be using a single head at a time, thus not allowing for the power boost.
If we look at the aesthics, the idea of three heads DOES seem to suggest a potent mixed attacker. Of course, such things were unheard of back then, especially out a Normal/Flying type, however currently I believe that Dodrio does stand to be a powerful quick, potent mixed attacker. Grant him Pure Power and a wider movepool and you could make him just that.
So, what do we do here? How close should we follow aesthics, and do we ignore the fact that everyone hates HAX and just create another potent user of it? Do we stick close to aesthics and forget about serene grace?
Even if we ignore aesthics, I think the best option though, when I really give it a long thought is clearly the mixed sweeper with Adaptability/Pure Power. Why is this interesting? Because both of these abilities essentially turn the pokemon into two completely different animals. Keep in mind, we would use Pure Power to boost its attack stat while investing its its Special Attack and Speed. So, as Bill Nye the Science guy once said, please consider the following.
As dodrio runs pure power, its able to run as a potent mix sweeper, though its clearly walled by steel and ghost types, though it fears few other walls. Its fast and strong enough to take out a good deal of Pokemon. However, from the moment its out, the opponent has to ask themselves a question, is this Pure Power Dodrio, or is this adaptability dodrio? He doesn't know exactly, either one would be a good switch in to this pokemon. What do I do? He switches in his Blissey, predicting a pure special sweeper running adaptability, opting not to bring out his Metagross, only to find it destroyed by a Return!
Now, THIS is what Dodrio could be, a pokemon with two distinctive and Pokemon defying abilities that it can't take advantage of at once, but it can abuse its opponent in the always fun game of GUESS OR DIE. Now, compare that to a Pokemon that just sits around attempting to get a Freeze off of Tri-attack, doesn't sound nearly as interesting, or as plausible for Dodrio, does it? Clearly THIS is the option we want to take Dodrio, as it fits both aesthically, but we make a viable Pokemon who commands a great deal of skill to use and to fight against.
As for the movepool and the new BST, I say on his stats he is mostly fine, flip Attack and special attack, nerf attack down to 45, boost Special Attack up to 115 and we've got ourselves a real contender here. He's not faster than most sweepers, though his Agility takes care of that, and if he wants the most out of Pure Power, he'll be force to run Max Attack, limiting his options.
As for his movepool, he'll need the obvious lighting attacks, and seeing as how he can learn Tri Attack, each signifing one of his heads, I think its a given that he should learn lighting, fire, and ice attacks, if just the most basics. I question if we should give him Sucker Punch (Sucker Punch is NOT a punch, keep that in mind, its original name Surprise Attack), because he needs SOMETHING to do against Sharpedo. I believe that Sucker Punch would be too strong an attack under full blast Pure Power, so Vacume Wave would probably be the better option. Its useful in both the mixed variants AND the Special varriants. You could also give him Extreme Speed. Yes, Adaptability and Extreme Speed sucks, however running on a Base 45 Attack isn't going to get you very far, he'd have to run Pure Power if he wished to get anywhere with Extremespeed. I say we leave Close Combat to Staraptor and instead give him Earthquake, hell, I thought he knew Earthquake in the first place. This gives him options against steels. I don't believe he could shut down every wall at once and still run a fully competent set, even in the Pure Power mixed set, but given the access to Thunderbolt, Earthquake, and Flamethrower does grant him a wide array of options in dealing with steel types.
EDIT- In Summary
Dodrio- Pure Power/Adaptability
Attack- 45
Special Attack- 115
Movepool additons-
Extreme Speed, Vacume Wave, Thunder Bolt, Thunder, Flame Thrower, Fire Blast, Ice beam, Blizzard and some other special moves that you guys see fit.