can I use "not only...but also" in the following sentences without "also"
1- I like not only strawberries but (also) bananas.
2- We walked through the hills not only when it was sunny, but (also) when it was raining.
3- The government was not only effective in lowering taxes, but (also) helped to reduce unemployment through careful measures.
4- It was not only fun, but (also) educational.
5- They were not only friendly, but (also) helpful.
In the construction, "not only x but also y", y adds to x.
In the construction, "not only x but y", y extends x.
"We were offered not only strawberries, but also bananas."
but also (heh-heh)
"The paper was not only crumpled but soiled and torn."
In the latter situation, "not just" is more common than "not only".
"My cheap thesaurus is not only terrible, but also terrible." (old joke)
I am not sure there is a hard and fast rule about the "not only... but also" construction, but my instinct when looking at your example sentences is that only #2 is completely natural without the "also" included, while 1, 3, 4, and 5 are various degrees of weird.
So if we examine what makes #2 different, I'd say that it's the fact that, in number two, the two ideas being contrasted – "sunny" and "raining" – are very close to direct opposites. If you read "not only when it was sunny," you can reasonably guess how the sentence will end, even if you're not totally sure which word it will be (rainy? cloudy? overcast? gloomy?).
Contrast that against #1, where we are comparing strawberries and bananas. First off, bananas are one of a zillion fruits; second, there's no such thing as opposite of strawberries (besides no strawberries); and finally, depending on the context, the second half of the sentence might not even need to be about another fruit at all. It could plausibly say "I like not only strawberries but also Ferraris." I'd posit that that's the reason #1 sounds not just unnatural but actually ungrammatical to me.
Sentence 3 suffers from a similar problem as #1 in that we can't really make a guess what the end of the sentence will be by reading only the first half because governments can be helpful for many different things.
Sentences 4 and 5 are somewhere in the middle in terms of naturalness. The fun vs educational dichotomy in #4 is common enough that that sentence sounds decent enough to me, but still just a bit weird. Similarly #5 I think is fairly sensible, but just slightly unnatural. I'd say both 4 and 5 are grammatical but unnatural.
You can't omit "also", no. You would still be understood, but it wouldn't really make sense.
The word "but" contrasts two things. In the first example, you are not contrasting strawberries and bananas. You are contrasting "not only" with "also".
Sentences 4 and 5 can have "also" omitted. The reason for it is straightforward when you think about it.
When you describe an object using multiple adjectives, you can combine them using conjunction "and". For instance, take the following sentence:
The apple was juicy and delicious.
Juice and delicious both describe the apple, but more importantly, the "and" used to combine them is not bridging two clauses or sentences together. It is strictly being used to combine adjectives.
Just like "and" to combine adjectives, you can use "but" to combine adjectives which starkly contrast one another.
The apple was sour but delicious.
It is in this case that "also" can be omitted, because in that case, it is auxilliary. In your other sentences, it is not being used to bridge two adjectives, so the also is needed to suggest that the contrast is to say "yes, this, but in addition to this also this". In other words, you're adding emphasis that there is more than one so the "also" is needed.
