What alkali and alkaline earth metal oxides will turn moist red litmus blue and finally white?
The standard oxides $\ce{Li2O, MgO}$ and $\ce{SrO}$ are water soluble and hydrolyse to form hydroxides and a basic solution. $\ce{BeO}$ is insoluble in water.

$\ce{RbO2}$ is a superoxide which in aqueous solution undergoes disproportionation to $\ce{O2}$ and $\ce{OH-}$ so will give a blue litmus test. 

The peroxides $\ce{Cs2O2}$ and $\ce{BaO2}$ react with water to give hydrogen peroxide and the hydroxides, so again a basic solution(source). The hydrogen peroxide produced will bleach the litmus paper.

$\ce{KO3}$(Potassium Ozonide) is highly unstable, decomposes in water to $\ce{O2}$ and $\ce{KOH}$

The oxides which will NOT decolorize litmus are $\ce{Li2O, MgO, BeO}$ and $\ce{SrO}$. The peroxides ($\ce{Cs2O2}$ and $\ce{BaO2}$), the superoxide($\ce{RbO2}$) and the ozonide($\ce{KO3}$) will decolorize litmus.