How does order-preserving encryption work on string?
Paillier cryptosystem has the property that the product of 2 ciphertexts decrypt to the sum of the plaintexts.

Strings are integers. Only that they are usually large. So this algorithm is also available for strings.

This algorithm doesn't allow you to find encrypted string in a ciphertext.

If you want an encryption scheme in which you can do any operation with the ciphertext, see homomorphic encryption.