You can play GC burns with cMIOS, but it's not really recommended anymore as Nintendont is far more convenient and has more features.
Is the Wii softmodded with a USB loader? If so you can use the same USB loader to play GC games from USB, but it might need to be updated and you'll need to download Nintendont and put it on the SD card.
If it's not softmodded yet, grab ModMii, it will guide you through the process, after that all you have to do is download Nintendont and put it on the SD card and enable it in your USB loader settings and it should just work. GC isos go in the "games" folder on USB IIRC, regular Wii games go in "wbfs", but you should use Wii Backup Manager to transfer Wii games and it will place them in the correct location and convert them to the correct format automatically. The HDD needs to be FAT32 formatted for GC games (32KB or 64KB cluster size preferred)