Literally, it would be closer to “I like juice of strawberries” — sútha is both the nominative plural form and the genitive plural form. The genitive singular is used for some fruits (e.g. sú seadóige [“grapefruit juice”, literally “juice of a grapefruit”]), and the genitive plural is used for others (e.g. sú úll [“apple juice”, literally “juice of apples”]).
Speaking solely from my own experience, I think it's very common in English to use words for various fruits as countable or uncountable nouns. Just as the word "fruit" itself can be countable or uncountable. It may be less common to treat "strawberry " as uncountable in Irish English, but in my opinion it's not wrong.