Can I suggest you read about key management? Generally speaking the private keys for most crypto currencies (if not all), are valid across the board.
However, wallet implementations differ because the addressing part of the respective chains is different, and wallet implementations do not in every case imply downloading the blockchain.
In addition communicating on the various networks to submit transactions is not trivial for a novice.
It is possible to create a so-called "trusted node" which your app communicates with in order to transmitt transactions to the various blockchains, and from which it receives balance information. You would have to set up your own communication protocol and your trusted node(s) would have to be available 24/7.
There are quite a few topics even in this short description - and it would be impossible to explain these in depth and the differences in all crypto currencies or the ways in which this could work. Also perhaps ead a few of the Wikis for each of the currencies you are interested in.
EDIT : In answer to the question about Jaxx - it does not look like it supports any other Ethereum tokens yet. Only the DAO as far as I know.