Ho-Oh

You can obtain Ho-Oh by doing the following:

Talk to the NPC in black at Saffron City Pokecenter.

He will give you a riddle/list as follows:

{Mr. Weirdo. Opera. Tongue. Supercomputer...} Which means:

{Mr. Mime. Jinx. Lickitung. Metagross}

Have these four pokemon in your party and an empty spot and he will give you Ho-Oh. (And if you're lucky, Ho-Oh will be shiny.)

You can obtain Lugia by doing the following:

Talk to the NPC in black at Cinnabar Volcano Pokecenter.

He will also give you a riddle/list as follows:

{Lazy bear. Dragonfly. Doctor. Fire bird. Magnets...} Which means:

{Snorlax. Flygon. Blissey. Moltres. Magneton.}

Have these 5 pokemon in your party and an empty spot and he will give you Lugia. (Could also be shiny.)