How can I clean solid sulfur and its oxides from test tube?
Since you stated:


  I'm not a chemist, so I don't have any strange chemicals at home.


you will neither have facilities for their proper storage and  waste management. 

Consequently, the only reasonable solution is: Get some new test tubes (about 0.20 Euro for a 160 x 16 mm tube), but don't risk your own health or pollute the environment by messing around with carcenogenic ($\ce{CrO3}$ in $\ce{H2SO4}$) or neurotoxic ($\ce{CS2}$) agents.