If by alumina you mean Aluminum Oxide the shelf life is indefinite if kept dry. If you mean Aluminum powder going by the information provided by Ron as reactions with Al powder can get nasty.
The others metal oxides if they are the highest oxidation state should have an indefinite shelf life if kept sealed and dry.
If they are fine powders they may tend to clump unless agitated.
Usually if there is any restrictions on storage it will be on the MSDS data or the product cut sheet.