The only options are to hack or trade.

Both are obtainable in Navel Rock(an island between Floe and Chrono Islands in the Sevii Islands), but you need the Mysticticket(event item) to get there.

OR

You can trade with another Pokemon game using the Link Cable.

You can try to find somebody to trade you one. If that does not work, pay attention for another event for them may occur near your town. That may also not work, so you are then left with the options of buying a hacking device such as an Action Replay or Gameshark, or buying other games for gamecube and using the legitimate method of obtaining them.

I am pretty sure that this is impossible without getting a hacking device, going to a special event, or getting additional games for other consoles etc.

You can buy a cheating device (since you missed the events). An Action Replay or Gameshark would work best.

To get Lugia and Ho-Oh, you must trade from XD and Colloseum respectively. Either that, or use a cheating device.

Yep, it's been said. To get them legit(like me) you have to get them from the two Gamecube games. Lugia shows up in the main story of XD, while Ho-oh requires a lot of effort in Colloseum.

You used to have to go get a mystic ticket from a nintendo special event, but they don't do those anymore for this game iirc. The only alternative to legitimately get them is to trade from XD and Colosseum as someone else already said. You can always use a gameshark/action replay to cheat and get them, but where's the fun in that :P

They're on island 8

You need to goto japan and during an event were they give you the special ticket or have the warp game shark code.

^Which is long over. So just Gameshark it or get a trade for it.

You need a special ticket or a game shark to get them.