The challenges associated with poverty measurement in an axiomatic framework, especially with cardinal variables, have received due attention during the last four decades. However, there is a dearth of literature studying how to meaningfully assess poverty with ordinal variables, capturing the depth of deprivations. In this paper, we first axiomatically characterise a class of additively decomposable ordinal poverty measures using a set of basic foundational properties. We then introduce, in a novel effort, a set of properties incorporating different degrees of poverty aversion in the ordinal context and characterise relevant subclasses. We further develop related stochastic dominance conditions for all our characterised classes and subclasses of measures. We demonstrate the efficacy of our methods using an empirical illustration studying sanitation deprivation in Bangladesh. Finally, we elucidate how our ordinal measurement framework is related to the burgeoning literature on multidimensional poverty measurement.