The orientable Euclidean orbifolds were described in section 7 of this paper of Dunbar.

To complete the list, note that every crystallographic group has an index 2 orientation-preserving subgroup. The corresponding orientable orbifold quotients will be realized as 2-fold orbifold covers of the non-orientable orbifolds. So one needs to look over Dunbar's list, and find all of the orientation reversion involutions of the corresponding orientable orbifolds to find their non-orientable quotients.

For the orbifolds with underlying space $S^3$, there are two possible orientation-reversing quotients: a reflection, and a suspension of an antipodal map. They admit quotients the ball and the suspension of $\mathbb{RP}^2$ respectively. So one needs to go through the list and determine which of these admit reflection or antipodal symmetries. For example, due to the well-known fact that the figure-8 knot is invertible, the label 3 figure-eight orbifold in Table 4 admits a quotient by a suspension antipodal map. For the first 4 examples in table 4, there is a reflection fixing the 1-skeleton of the simplex with quotient a Coxeter group. Some of these also admit further reflection symmetries.