The ArcGIS (by Esri) have a tool for calculate The Anselin Moran. I guess that you can use this tools for your study. I don't know Oden's, but if you wanna know spatial dependence, this tool will be useful.
Oden's I is an adaptation of Moran's I that takes into account the fact the data are aggregated (e.g. comprised of a numerator and denominator). Both Moran's I as well as the Local Indicator of Spatial Autocorrelation (LISA) of Anselin do not account for population size, and hence can be biased when applied to rates calculated for local areas. Oden's I is a more powerful alternative, but does require you have the numerator and denominator data for each local area. It can be calculated in ClusterSeer, available from BioMedware.
If you have resolved the spatial relationship, namely the weighted matrix. Sure you can use R software for Oden's I. There are some packages of spatial economics in R codes for reference.
SANET of Prof.Atsu Okabe is also interesting. SANET is a toolbox for analyzing events that occur along networks which you can adapt it to your purpose.