The inversion does not normally carry over to subsequent independent clauses, so
Not only were they tall, but they were also strong
is the correct version.
Subject-auxiliary inversion occurs in declarative clauses only when certain types of element are put in front position. Negatives are one very obvious type of element that trigger subject-auxiliary inversion when fronted:
Never had I seen such chaos.
At no stage were they in danger.
"Not only" is clearly negative, but even when used alone, "only" has the same effect:
Only when I counted the money did I realise the error.
"Only" is not negative, but it is semantically close to a negative, in that only John liked it, for example, entails No one other than John liked it.