A cockatiel that is lethargic is a sign of a serious underlying decease, and requires immediate veterinarian attention. Birds have a very fast metabolism and time is the essence to get a diagnosis and get your cockatiel treated as soon as possible.
Other serious diseases might be the reason, like a bacterial infection that might show flu like symptoms. If your tiel is wobbling the head such as dizziness, sitting on bottom of the cage, unable to fly, it is often coming from toxicity's like heavy metals. If he is confined in the cage, that means it could come from the cage, other toys or metal things in or attached to the cage.
"Food poisoning, fumes in your house (specially from cooking or cleaning agents used in your house), or a cold can contribute to your bird being lethargic."
A great deal of birds that wobble their head an appear dizzy, are frequently related to cleaning their houses or bathrooms and the fumes from the cleaning agents propagate throughout the house. Make sure that when cleaning your bird is in a different room and that your hose gets ventilated for hours before closing the windows. Candles, and plug in room deodorizers, can also make your cockatiel very sick.
You might have heard the term 'Canary in a Coal Mine'; in the early mining days miners would carry caged canaries down into the mine tunnels with them. If dangerous gases such as carbon monoxide collected in the mine, the gases would kill the canary before killing the miners, thus providing a warning to exit the tunnels immediately. Birds have an incredibly fast metabolism and their respiratory system is very fragile. To the average person a small smell or fragrance is nothing, but for a bird it can be deadly.
As always the information offered here is to provide guidance and is not intended to be a substitute for the good advice provided by your own avian vet. When in doubt always consult your own veterinarian.