if length of each string is finite lets say N, we can enumerate it with sets of natural numbers, you can enumerate by beginning with N boxes, fill the first box with 2 possiblities, 0 or 1. second box with 2 more possibilities so 2x2. and so on. so they are countable and finite as well. in this case there are 2x2x2...2 = 2^N strings possible, at the last box, you will exhaust all the possiblities, and cover all possible strings. meas it is finite. this is only possible if length is finite.
but if length of each string is itself infinite, we cant count it. it follows from Cantor’s diagonal argument. If you arrange all the strings as per their digit, there is always one more infinite string that is different from all other strings, you can always form it so that it differs from string1 in 1st bit, from string2 in 2nd bit and so on. that is uncountable set.