Nadian
Sounds like you are playing Silver, Gold, or Crystal. Unfortunately, I am unfamiliar with those games, although may I suggest checking out GameFAQs?
if it's GSC, then that was the last cartridge I owned before diamond. (borrowed the various other games)
Catching the beasts is unnecessary to obtaining Ho-oh or Lugia (in GS, but not Crystal). This is important as to which version your playing though.
If your playing Silver, you have to talk to someone in Pewter City to get the Rainbow Feather.
If your Playing Gold, you have to talk to the Radio Director after clearing out the Rockets.
But, if your playing the game I think you are (crystal) Go meat Eusine in Celadon City (pokemon center) then talk to the Wise Trio in the tower to get the feather. or, at least that's what I remember, it's been years since I played those games.
So, uh, if your playing Gold you don't need to beat the elite four. if your playing silver or Crystal, you'll need to beat the Elite four.