This is only possible in the postgame, after you've beaten the final boss. While you can kill the Drake before the postgame, you won't see a Wyvern and Wyrm until later.
LOCATIONS:
DRAKE: There is always a drake in DevilFire Grove. The grove is located in the Southwestern region of the map. There is a small lake, Lake Hardship, in this area. Northeast of the lake is the exit from the Ancient Quarry, Northwest of the lake is The Shadow Fort, Southeast is a camp, and the drake is on the Southwest bank of Lake Hardship.
WYVERN: You're supposed to have to travel all the way to Bluemoon Tower to find the wyvern, but I found a shortcut. In the postgame, go to Windbluff Tower, which is directly North of Gran Soren. Just South of the Tower is an embankment. At night, the wyvern flies over this area. I shot an arrow at it to get its attention.
EDIT: The earliest you can fight this Wyvern is if you walk from Cassardis to Gran Soren in the post game. The wyvern will be waiting for you outside Gran Soren's Southwest gate. If you don't want to fight him, can't beat him yet, or if he flies away, he can always be found at the location above.
WYRM: In the postgame, follow the main quest "A Warm Welcome" in Gran Soren. While this quest will prevent you from ever entering the Noble District or Castle again, the trade-off is that you can enter the Everfall. When you enter, you will be able to hold the right trigger to grab a ledge. After entering "Chamber of Confusion" and fighting the Evil Eye
you can float down the Everfall. On the East side is a ledge which you can press right trigger to grab on to. If the door tells you you're at the "Chamber of Distress," you're in luck. Kill the wolves and harpies inside and enter the main chamber to find the wyrm.
STRATEGY:
My party was a ranger (myself), a fighter (my pawn), and two rented pawns who were a sorcerer and a mage. My pawn and I were level 44-46 and my rented pawns were level 59 & 60. I hid behind cover and shot tenfold arrows at their hearts (the drake's and wyrm's hearts are under their chests, but the wyvern's heart is on its back). I revived party members and hoped for elemental buffs. None were as difficult as the final boss, and these are similar, yet weaker, enemies. Stay out of the line of fire, avoid their breath attacks, and let your pawns take the brunt of the damage.
I'll gladly add strategies and give credit to others. Please PM me or leave comments of what you'd like to contribute & I'll give you credit.