How can I check if this mystery compound is strontium bromide?
Relying on the fact that the compound is almost certainly a strontium compound, I'll look at the reactions with sulfuric acid of the specific anions:

$\ce{SrBr2}$

$$\ce{SrBr2 + H2SO4 -&gt;  2HBr + SrSO4}$$
Both compounds $\ce{HBr}$ and $\ce{SrSO4}$ are white or colourless. BUT! concentrated sulfuric acid oxidizes $\ce{HBr}$ to bromine gas:
$$\ce{2 HBr + H2SO4 → Br2 + SO2 + 2H2O}$$
And bromine gas has a yellow/red colour. So your compound is strontium bromide.

$\ce{Sr(NO2)2}$

This is a yellow compound. As you mentioned, the compound was white, so it isn't strontium nitrite.

$\ce{Sr(NO3)2}$

$$\ce{Sr(NO3)2 + H2SO4 -&gt;   2HNO3 + SrSO4}$$
Both compounds $\ce{HNO3}$ and $\ce{SrSO4}$ are white or colorless. After looking some more stuff up, it turns out that sulfuric acid and nitric acid don't react (at room temperature) to produce any yellow/brown $\ce{N2O4}$ gas.