The two pages below display my current candidate for the algorithm for computing annihilators and associated varieties for the groups SO(p,q) and Sp(n,ℝ).  This algorithm is still experimental.  It may not be correct in all aspects.  I welcome feedback.  Please contact me at devra.johnson at verizon.net.

There is a block of representations for SO(p,p+1), and one for SO(p,p), which are not covered by this algorithm.  Instead, you would use the algorithm for their dual representations.  For that, see the Sp(p,q) Algorithm and the SO*(2n) Algorithm.