This is one of the more extreme shifted clay-tile lined chimneys I've ran across. Usually on older homes from the 1940's-1960's, they'll have a clay-tile liner. Most often, the mortar joints have deteriorated out allowing the flue gases a secondary avenue to flow. Shifted liners and cracked liners are found frequently as well and pose the same problem. Whenever there is a breach in the liner, there is a threat of catching the house on fire and having flue gases leak into the home which can lead to carbon monoxide poisoning. Because this is connected up to the furnace and water heater, this chimney can easily be resolved by having either a Certified Chimney Sweep or licensed HVAC Contractor install a metal flue down the center. If this were for a wood fireplace, it becomes a lot more complicated and you definitely ONLY want a Certified Chimney Sweep tackling the job.
Read tips on Avoiding A Chimney Fire.