  We use analytic calculations of the post-recombination gravitational effects
of cosmic strings to estimate the resulting CMB power spectrum, bispectrum and
trispectrum. We place a particular emphasis on multipole regimes relevant for
forthcoming CMB experiments, notably the Planck satellite. These calculations
use a flat sky approximation, generalising previous work by integrating string
contributions from last scattering to the present day, finding the dominant
contributions to the correlators for multipoles l > 50. We find a well-behaved
shape for the string bispectrum (without divergences) which is easily
distinguishable from the inflationary bispectra which possess significant
acoustic peaks. We estimate that the nonlinearity parameter characterising the
bispectrum is approximately f_NL \sim -20 (given present string constraints
from the CMB power spectrum. We also apply these unequal time correlator
methods to calculate the trispectrum for parrallelogram configurations, again
valid over a large range of angular scales relevant for WMAP and Planck, as
well as on very small angular scales. We find that, unlike the bispectrum which
is suppressed by symmetry considerations, the trispectrum for cosmic strings is
large. Our current estimate for the trispectrum parameter is tau_NL \sim 10^5,
which may provide one of the strongest constraints on the string model as
estimators for the trispectrum are developed.
