What is the difference betweeen 'believe strongly' & 'strongly believe'?
Is 'I believe strongly' a correct usage?
What is the true difference between these two? Different emphasis?
As was previously stated by @RobbieGoodwin in a comment: No; there's no difference except personal style. Those phrases always have the same meaning.
There may be times when one sounds more natural than the other, but we'd need more context to figure that out.
There are several guides (here is one from the Cambridge Dictionary) which say that a mid-position adverb should normally be placed before the verb
strongly believe
There are specific circumstances when after is preferred, but I don't think any of those listed apply. As with the Pirate's Code, these are guidelines rather than absolute rules... but you won't go far wrong if you treat them as rules.
Looking at this NGram graph, it seems that the before position is the preferred option by a factor of three.
I was surprised that the proportion of after instances was so high, so I checked individual instances. One that I can understand is where the word pair is followed by enough
A child must believe strongly enough to hold on even when he doesn't want to. -This I believe, Dan Gediman, 2012
In this case, the adverb is not just strongly, but a complete adverb phrase "strongly enough to hold on even when he doesn't want to", and adverb phrases usually go in the final position.
When the word pair is followed by a long adverbials, for example a prepositional phrase, this NGram graph shows that the after position is marginally preferred.
Most of the remaining instances of after involve a that-clause, though for the majority of that-clauses, the before position is preferred.