My Closet Smells Like Sewer - How To Fix?
It's normal to smell gas in the plumbing downstream of any water trap. The trap provides a plug to prevent the gas from entering living space, but it's free to roam elsewhere, including out the vents on your roof. 

You may be able to simply tighten the cleanout plug enough to get it to self-seal. Use the back of a ChannelLock, adjustable wrench, or large open-end wrench inside the slot to get good torque. 

Otherwise, use thread paste or PTFE tape (3-5 wraps in the correct direction) to provide a better seal. I wouldn't use caulk, as it makes a mess and isn't reusable.