PS2ESDL plays games installed with USBUtil or USB Extreme, read the readme file that comes with it for more info.
Possible reasons I can think of why games won't play from USB:
The game needs a mode or modes enabled with OPL
The USB drive is fragmented
The USB drive has file errors or bad sectors
The USB device isn't fully compatible with the PS2
The ISOs are corrupted or incomplete
Errors with the applications on the memory card, re-installation may help
The game may work better with OPL as an ISO in a folder, or installed with USBUtil or USB Extreme
The game doesn't work with with earlier revisions of OPLv8
The game doesn't work with OPL at all, but does work with PS2ESDL
The game can't be played from a USB device, try burning to disc or playing from computer network or internal HDD for Fats
The game can't be played as a backup, buy the game
PS2 hardware problems, get a new PS2
I've told you everything I know about how to play games from USB, I can't help you any further.