Answer
$T_3 > T_1=T_4 > T_2$
Work Step by Step
The tension in the string provides the centripetal force to keep the objects moving in a circle. In general, the centripetal force is: $F = M~\frac{v^2}{R}$. We can write an expression for the tension in each case.
$T_1 = m~\frac{v^2}{r}$
$T_2 = m~\frac{v^2}{2r}$
$T_3 = 2m~\frac{v^2}{r}$
$T_4 = 2m~\frac{v^2}{2r} = m~\frac{v^2}{r}$
We can write the tensions in order from largest to smallest:
$T_3 > T_1=T_4 > T_2$
