Zapdos, Moltres, and Articuno represent the forces of lightning, fire, and ice. As Prof. Oak stated in The Power of One, an electrically-charged steam current has the power to flood the planet. This is basically what the "Beast of the Sea" was, caused by an imbalance of power between the trinity of forces. Lugia, having ocean-related powers in combination with being a Psychic type, allowed it to calm the birds. Not on its own, of course; Ash needed to get the orbs from each island and place them in a single shrine. I suspect that these orbs were charged with the elemental powers of the respective birds, and the sound waves from Melody's ocarina or Lugia's cry caused the radiation from those orbs to harmonize, which in turn would harmonize the birds themselves, restoring the balance and "calming the 'Beast of the Sea'". Such a form of radiation would only affect Articuno, Moltres, and Zapdos in this way. It would be just like light from a flashlight to anyone else.
In Ecruteak City, we learn that Lugia and Ho-Oh lived there atop twin towers in ancient times, but human greed and lust for power chased them away. If I remember correctly, the Tin Tower is where Lugia lived, and the Brass Tower (now the Burnt Tower) was Ho-Oh's perch. Lugia probably evolved (not in the Pokémon way) to adapt to the ocean, thus why you find it in the Whirl Islands. Ho-Oh probably decided to return to the Tin Tower, since it was the only tower standing and sensed your kindness.
Again in Ecruteak, you learn that Ho-Oh has a connection to Entei, Raikou, and especially Suicune. It seems to me that the legendary dog trio are judges, racing across the land not just because their power is incredible (and yet they're all BL/OU? What the hell?), but also because they were watching us humans. Then you come along, capture/defeat all three, and Ho-Oh understands that humans aren't beyond redemption, and thus flies to Tin Tower and awaits you.
Speaking of Suicune, there's a connection with the Unown here. They never were considered like this before, but perhaps Unown can be a legendary Pokémon? Also, if you've seen Spell of the Unown, you know that the Unown come from an alternate dimension... Perhaps the same dimension Giratina hails from? Maybe the Unown were created so that humans could better understand Pokémon simply by spelling certain things out.