**Hints for the force**

1. The electrostatic force $d\vec F$ on a small segment $dl$ of the rod given the field $\vec E$ of the other rod is
$$
  d\vec F = \lambda\, dl \,\vec E
$$

2. Determine the field of one rod, and use the above expression to integrate the force it exerts on the other rod.

3. This is a 2D problem since, by symmetry, the force is in the plane containing both rods.

**Hints for the torque**

1. Take the point at which both rods are joined as the origin, then the torque on a small segment of one rod due to the field of the other is
$$
  d\vec \tau = \vec r\times d\vec F
$$
where $\vec r$ is the vector pointing from the origin to the segment.

2. Integrate to find the total torque.

**Addendum.**

I started solving this problem, then I got to integrals I needed to compute to determine the electric field of one rod at a general location on the other, and I realized that there is no solution to this problem as stated.  The force between the two charge elements at the end of each rod where they are joined is infinite (because the distance between then is zero).  You can make this problem well-posed by considering a charge densities $\lambda_1, \lambda_2$ that goes to zero sufficiently quickly at the point where the rods are joined so that the integrals you have to perform don't diverge, but that would be a different problem.