  Equations of motion of null cosmic strings near black holes, or other massive
sources, are solved exactly in the weak field approximation. The stress-energy
tensor of a null string in a curved spacetime is introduced and used to show
how scattering by black holes transforms linear and angular momenta of the
string. The corresponding recoil effect of a black hole and change of its
angular momentum caused by a null cosmic string are calculated. For a null
string, its energy $\mu$ per unit length evolves along the null direction of
the string trajectory. The evolution of $\mu$ is connected with a string
optical scalar $Z$. Optical properties of null strings are that their energy is
concentrated on caustics, where $Z$ has poles. String parameters $\mu$ and $Z$
capture important features of the spacetime where strings move. Explicit
dependence of $\mu$ and $Z$ on the strain and Bondi news tensors of
gravitational wave background, mass and angular momentum aspects are
established, near the future null infinity, up to the 4-th order in expansion
in an inverse null parameter in asymptotically flat spacetimes.
