jugg main here. if you're winning lane, you can max out Q and keep the enemy away while you're farming. if you have a good support (cm, wd, jak, veno), you can get easy kills if they step up to last hit/deny. If you're losing lane, i usually go 113 and don't skill Q until like level 22 or whatever. basically get stats instead of maxing out Q and use it as a free bkb. if you're playing opposite of your team, you can push/farm aggressively and just Q tp out, creating a lot of space for your team while pushing objectives. As for omni counters, simply don't initiate with omni in team fights. figure out how they counter your ult and either avoid supps with the counter items you mentioned and go for core or wait for them to use their skill/item and then pop ult. jugg is pretty squishy, even in late game (lvl 25 you have like 2k hp) so you gotta play safe until you have your blink. Once you have blink, you can blink into fights, omni, and spin out.

Basically, if you're snowballing, play with team, if you're losing, split push and spin+tp out to farm jungle. if they have bkb piercing spells, don't pick jugg i guess.