In Korean, both "should" and "have to" are expressed by the same grammatical structure: 아/어야 되다/하다/지(colloquial)/겠다(future tense equivalent). Koreans do not identify the difference between "have to" and "should" in their daily life as they are conveying very similar meaning. The only difference of these two words in English is the extent.
If you want, you may also use another grammar: ㄹ/을 필요가 있다. But its correct translation should be "need to".
Example: 숙제를 오늘밤에 할 필요가 있다. -> You need to finish your homework tonight.(changing "need to" to "have to" does not seem to make a difference in this case)
ㄹ/을 수밖에 없다 could be similar, but its meaning should be "can only".
Example: 이 곳에서 떠날 수밖에 없어요. -> I can only leave this place. (I have to leave this place.)
Addressing the expression "You are recommended to...":
I think using (으)면 좋(겠)다 will best fit the meaning. Ex: 지금부터 공부하면 좋겠어.
If you want to express the word "strongly", you may use 강하게, or I saw 강력히 being used in articles. But combining it with the grammatical principle quoted above may not be a good idea. You may use the word 권하다, but it is a bit authoritative.
Ex: You are strongly recommended to think twice.
다시 생각해 보는 것을 강력히 권합니다.
Hope this helps.