In the paper below Rosenstein gives a complete characterization of $\aleph_0$-categorcial theories of linear order.
Rosenstein, Joseph G. $\aleph _{0}$ℵ0-categoricity 0$-categoricity of linear orderings. Fund. Math. 64 1969 1–5. You can also find the result, and many other gems, in Rosenstein majestic text on linear orders. 1 In the paper below Rosenstein gives a complete characterization of$\aleph_0$-categorcial theories of linear order. Rosenstein, Joseph G.$\aleph _{0}\$ℵ0-categoricity of linear orderings. Fund. Math. 64 1969 1–5.