We have lived in our new home for 2 1/2 weeks, and the toilet in the master bathroom has been gargling since the first time I flushed it; so I have been using the guest bath more than the master. Today I used the master toilet and it gargled again and a strange, burning type smell has been coming from the toilet (not too strong) but strong enough. When I say gargle it makes like a gulp, gulp, gulp.. Then the water would get really low... But also today, while taking a shower in the master bath I noticed the smell coming from the shower too (burning-type smell). None of the other drains, toilets have been acting strange to my knowledge, please advise if this sounds like a clogged vent. Thank you very much!

You have described a blocked lavatory vent. The sound you hear is air being pulled through the toilet bowl to relieve the suction caused by the discharge,
The solution would be to snake the vent from the roof. Put out enough snake to reach the base and 20 feet more. Good luck, Tom