I'm not an expert, but from what I read, nimbus is a word normally associated with rain-bearing clouds. This happens when moist air is lifted up and condensation occurs (The mechanisms for stratus and cumulus based rain is different: see CUMULUS VS. STRATUS). read more
The reason that we don’t have ‘cirronimbus’ clouds is that nimbus-type clouds are rain-bearing and cirrus clouds only occur above the freezing level and are fine, wispy clouds made of ice crystals - they never bear rain. read more
The reason we don’t have altonimbus clouds is because the alto- prefix simply refers to mid-level clouds and it’s quite rare for a nimbostratus cloud to occur with its base at that level. When they do they are still called nimbostratus. They just aren’t different enough to have their own designation. read more