It would help a lot if we knew what dewormer he was given. If a pill, it's usually either drontal or droncit. Drontal is supposed to treat both round worm and tapeworm, if I recall correctly. Droncit I know treats only tapeworm. Unfortunately, if he has round worm, drontal is not always effective. Where we live, the round worms are resistant, so it's useless.
I'm sorry, I don't know Oliver's background. Is this a rescue kitty? Or is he indoor/outdoor?
Either way, does he currently have fleas? Or have those been treated, and they're no longer a problem?
We've found the most effective way to treat (most) internal parasites is Revolution - a topical treatment. It also treats fleas (and supposedly ticks, though it doesn't do a very good job on the ticks). When you've finished three cycles of treatments every three weeks, then give kitty Droncit to kill the tapeworm.
The round worm life cycle is such that you have to give treatments every three weeks. Most of the poisons used to kill them, whether Panacur (a liquid), Strongid-T (a liquid), Revolution (topical), Advantage Plus (topical), or Drontal (a pill, often not effective for round worm though its supposed to be), treat the adult round worm. So you have to then let remaining eggs mature, and kill those adults (2nd treatment). And to ensure you got them all, a 3rd treatment is usually given. Thus the three week spacing between treatments. You also need to be very diligent about scooping litter, so the cat doesn't get reinfested from its own feces.
I have to assume this is the issue, because tapeworm is (usually) resolved with one treatment. Tapeworm looks like little bits of rice. It can ONLY be transferred to a cat via a host, such as a flea bite or eating a mouse or something. However, if the cat still has fleas, or is allowed outside to hunt, the cat will continually have the problem with tapeworm. So if the first treatment didn't stop the tapeworm, he's getting reinfested somehow, and you need to figure out the source.