Most Logitech software I've seen includes a removal tool.
Run that, then reboot.
Otherwise, the Logitech preference pane (control panel) will be in either /library/preference pane or (your username)/library/preference pane. Drag that to the trash. There's usually a kernel extension though for Logitech's keyboard/mouse software, and I'm not sure what that will be called, so probably best to simply use the uninstaller included with the software.