It takes practice to dodge his sideways skill but play against him often enough and you'll see it coming. As with most skillshots, walking towards the enemy rather than away (which they often plan you'll do) often works.
His ult does very strong damage, however it can be interrupted, pack a support with an interrupt (which is... most supports).
I find Sona to be very strong against him as she easily matches him poke for poke, hers is guaranteed, she has sustain, and her ult stops his. Most Vel'Koz support also pack AP runes so they're quite squishy, I've 1v1'd many of them successfully with Sona.
Nami does decent too, it's a skill match up but she has the edge with her sustain.
Soraka probably does well too but I don't play her so I can't really give you advice.