= Solution
A loop whose Klein deck transformation has odd $c$ has one closed lift to the orientation double cover; one with even $c$ has two. Thus the preimage of $\gamma_1$ contains one closed geodesic, while those of $\gamma_2$ and $\gamma_3$ contain two each.
In the torus unit square, representatives are
$$
\widetilde\gamma_1(t)=[t,0],
$$
which maps twice around $\gamma_1$;
$$
\widetilde\gamma_{2,1}(t)=[0,t],
\qquad
\widetilde\gamma_{2,2}(t)=[1/2,t];
$$
and
$$
\widetilde\gamma_{3,1}(t)=[t,t],
\qquad
\widetilde\gamma_{3,2}(t)=[t,1/2-t].
$$
All coordinates are taken modulo one. Hence the requested numbers are
$$
\boxed{1,\quad 2,\quad 2}.
$$
The two diagonal lifts of $\gamma_3$ meet over its self-intersection point but remain distinct closed geodesics.
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