You are playing Forrester & Bahkshi
Read the explanation of the auction carefully...
1NT = 10-13, may be off shape
x = EITHER penalties OR 5-card minor + 4 card major
xx = strong
after the redouble they explain they have only discussed continuations after an SOS or conventional redouble "no-one ever plays redouble as strong here". However, if the redoubler had passed, 2D would have shown 3-3 in the majors; with the redouble they aren't sure what it meant and it is possibly natural; however either way there is a strong inference that your RHO is short in clubs.
Pass over 2D = forcing, usually a penalty double
Double of 2D = prepared to defend 2Dx if opener has a penalty double ("take-out")
xx = SOS
Double of 2H = penalties
Do you double 2S?

Help

1NT x xx 2D
P P x P
P xx P 2H
P P x 2S
?