Q:

What determine the length of encrypted String in RSA?

I know about length of some small encrypted strings as: 160, 196 ..
What determines the size?

A:

The size in bytes of a single "block" encrypted is the same as the key size, which is the same as the size of the modulus. The private exponent is normally about the same size, but may be smaller. The public exponent can be up to to the key size in size, but is normally much smaller to allow for more efficient encryption or verification. Most of the time it is the fourth number of Fermat, 65537.
Note that this is the size in bits of the encrypted data. The plain data must be padded. PKCS#1 v1.5 uses at most the key size - 11 bytes padding for the plain text. It is certainly smart to keep a higher margin though, say 19 bytes padding minimum (a 16 byte random instead of a 8 byte random for padding).
For this reason, and because it is expensive to perform RSA encryption/decryption, RSA is mostly used in combination with a symmetric primitive such as AES - in the case of AES a random AES symmetric secret key is encrypted instead of the plain text. That key is then used to encrypt the plain text.

