The sale of the gas for human consumption has been illegal since May when the Psychoactive Substances Act came into force.
However, the BBC was able to buy several canisters of the drug, known as laughing gas, after contacting a dealer advertising it for sale on Facebook.
Two men have been arrested as a result of the investigation, police said.
According to research, nitrous oxide is now ranked the fourth most popular drug in the UK, excluding alcohol, tobacco and caffeinated energy drinks.
One woman told the BBC: "Every time you go out, if you go to a house party, it's always there.
"It probably should [concern me] but it's just become quite normal."
Another said: "It's a lot harder now to get it at clubs, but definitely at house parties it's everywhere."
Source: Frank
Experts said the use of the drug is potentially fatal.
Dr William Harrop-Griffiths, from the Royal College of Anaesthetists, said:  "When you breathe in nitrous oxide it is absorbed really quickly in to the body.
"It goes straight to the brain and it can cause unconsciousness within 30 to 45 seconds.
"The unconscious human being is at risk and if there are not people around to support their airways, support their breathing, you die as a result of unconsciousness."
According to research, there were 17 deaths related to the use of laughing gas in the UK between 2006 and 2012.
Following the BBC investigation, West Yorkshire Police said two men, aged 24 and 20, were arrested on suspicion of possession of nitrous oxide with intent to supply.
They were arrested after officers discovered nearly 5,000 canisters and 7,200 balloons at an address in Gipton, Leeds.
Both men were released on police bail pending further enquiries.
The BBC has approached Facebook for a comment on its policy surrounding the issue.
For more on the investigation watch BBC Look North (Yorkshire) at 13:30 and 18:30 GMT on 19 January.
Party drug nitrous oxide is being sold illegally across Leeds via Facebook, a BBC investigation has found.