It doesn't seem to me to be possible to use the adverb "strongly" in connection with the verb "try" but I can't figure out why not. It feels as it it ought to be possible but never sounds right. Is this a correct observation and if so is there a clear linguistic reason for this? The obvious answer is to use the adverb "hard", but why not "strongly"?
I don't think there is anything wrong with "try strongly" per se. It is just not the idiom that we use. In English, when I was a kid, we used to say "I did such and such by accident", most young people now say "I did such and such on accident". It is just a change in the idiom of the language.
If you said "try strongly" people would certainly understand what you meant, but it wouldn't seem quite right. I am reminded of a question someone else asked a while ago which I answered:
How does a learner learn what is right and wrong? Unfortunately, I think the only way is by reading, listening and speaking a lot of English with native speakers.
in the context of sports:
Sculthorpe raised hopes of a fightback with a typically strong try but a double from Brian Carney, Wigan's exuberant Irish flyer, put the seal on their night.
Bit of a stretch, since the phrase is strong not strongly.