My understanding of radiation is energy being emitted from a source. So much radiation would come out of a home gas or oil heater to become dangerous. I'm assuming infrared radiation.
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Solar radiation is pretty close to $1kW/m^2$. That's already borderline problematic for a human who is completely exposed. I would guestimate with a giant foam hand that $2kW/m^2$ for more than a few minutes is more than enough to give humans a bad time. You could, of course, test this experimentally with a 100W light bulb. What's the closest distance that you can hold your hand to it for all but a moment? Calculate the flux at that distance and you have a pretty good upper limit for the maximal tolerable exposure to mostly IR radiation before burns occur. You have to be very careful not to overdo it, of course. Your body tells you rather precisely when something is beyond the biologically tolerable, so listen to it!
The IR radiation from a gas heater is dangerous, but not for the reasons you seem to think. Each year nearly 500 people die as a result of space heater radiation http://www.nfpa.org/press-room/news-releases/2010/space-heaters-involved-in-79-percent-of-fatal-home-heating-fires. Granted, in the US, space heaters are almost always electric, but I'm sure there are the occasional gas heater incidents.
The problem is that the IR radiation (heat) from the heater sets fire to nearby materials, and the resulting fire kills people.
A bigger danger from gas heaters is carbon monoxide poisoning.
From 1999 to 2010, the carbon monoxide fatality rate in the US averaged about 430 per year. http://www.cdc.gov/mmwr/preview/mmwrhtml/mm6303a6.htm
According to this link http://www.physlink.com/Education/AskExperts/ae409.cfm to Johns Hopkins, "The majority of carbon monoxide exposures occur in the winter months and the most common source of residential CO-related poisoning is unvented supplemental heaters."