if you feel or believe in something strongly, you are very sure and serious about it:
I'm strongly opposed to capital punishment.
We strongly believe that she is innocent.
I'm strongly in favour of marriage.
in a way that is meant to persuade someone to do something
strongly suggest/advise/recommend something
Before taking action you are strongly recommended to consult an accountant.
in a way that is easy to notice:
The house smelt strongly of food.
! Do not say 'hold/grip strongly'. Use firmly or tightly: He gripped my arm tightly.