  Let $D$ be a DVR, let $K$ be its quotient field, and let $R$ be a $D$-order
in a quaternion algebra $A$ over $K$. The elasticity of $R^\bullet$ is
$\rho(R^\bullet) = \sup\{\, k/l : u_1\cdots u_k = v_1 \cdots v_l \text{ with
$u_i$, $v_j$ atoms of $R^\bullet$ and $k$, $l \ge 1$} \,\}$ and is one of the
basic arithmetical invariants that is studied in factorization theory. We
characterize finiteness of $\rho(R^\bullet)$ and show that the set of distances
$\Delta(R^\bullet)$ and all catenary degrees $\mathsf c_\mathsf d(R^\bullet)$
are finite. In the setting of noncommutative orders in central simple algebras,
such results have only been understood for hereditary orders and for a few
individual examples.
