Strange to say, I didn't feel any pain at all.

Literal

Strange story but [concessive-が], I [topic-は] any pain [even-も] didn't-feel.

何の~も~ない is the 'not any X at all' pattern — quantifier 何 ('any') + も + negative creates a strong universal negation. Here 何の痛みも感じなかった = 'felt no pain whatsoever.' The 何の modifies 痛み, restricting it to 'any kind of pain.'