Are there simple models of Euclid's postulates that violate Pasch's theorem or Pasch's axiom?

There are no simple models. To violate Pasch's Axiom in a Hilbert-type setup, we need to use a discontinuous solution of the Cauchy functional equation $f(x+y)=f(x)+f(y)$. Such a discontinuous solution requires (part of) the Axiom of Choice.

In ZF with added axiom that every set of reals is Lebesgue measurable, the Pasch Axiom is a theorem of a Hilbert-style axiomatization that leaves out the Pasch Axiom.

Remark: The first construction of a non-Paschian geometry that otherwise satisfies the full set of Hilbert's axioms is due to Szmielew. A proof that such a geometry must be of the Szmielew type was given by Adler.