How to prove Security of Onion Layers of encryption? CryptDB has Onion layers of Encryption to provide wider functionality from weaker forms of encryption. How do we prove such things are indeed secure ? Intuitively It seems ok. Are there any parallels in theory that is related say, security of multiple encryption schemes etc? or Universal Composability etc?

Is this same as Cascade ciphers ? Product Ciphers ?
In CryptDB, it is not really cascaded. According to encryption schema the layers are decrypted. At the end, the lowest level is the your security. 

The current layers are RND (Highest Security) , DET (For Joining queries), SWP (Search), HOM (Add), OPE (Sort) etc.  OPE being least secure as it allows more inferences about the underlying data fields than others. A data field that is encrypted all these Onion layers offer security only as strong as the weakest (OPE or similar) ! 

The fact that there is no need for the removal of the layer implies there is no need to layers.