I would also have suggested cleaning, but it sounds like that's not the problem. It could well be that the wiring or the insulation on the wiring is bad and causing the smoke. I would not recommend using it again. You could get a service tech in to check it out but if it's 16 years old you'd probably just be better off replacing it.

Most new ovens will do this the first time they're turned on. Oils left over from manufacturing process burning off. It could be that the oven was never used, so you basically have a brand new 16 year old oven. IF this is the case, the problem would be resolved by just using for a while and dealing with the smell. If this were a brand new oven you had just purchased I would suggest using the self clean cycle to speed up the process, and if there were any issues warranty would cover it, but since this doesn't apply to you, and you aren't sure of the source of the smell I wouldn't suggest doing that.

That could be a possible explanation for the smell. Having said that, I'm with weissman on this one. I don't want to suggest you just ignore it in case there actually is a problem.

I'm certainly not an appliance expert. But -if- it smells like regular cooking type smoke, then I'd look at cleaning any exposed heating elements, like the broiler coils. They may look clean, but really have a layer of crud on them.

If it smells more chemical/electric/plastic-y or just "not right" then I'd not use it until checked out.

Also make sure you have an appropriate fire estinguisher handy, and check that it is still properly charged.