Where are all the Bitcoin and other cryptocurrencies stored? 

Bitcoin are decentralized. This means to make a transaction you do not have to go through a third party. Traditionally, online financial transaction are made via a centralized third party such as a credit card, a bank or a payment processor such a PayPal. With cryptocurrency we exchange currency directly. Just as we would hand over cash from one person to another in the physical world, in the digital world we hand over encrypted nodes that represent value, peer to peer. Just as in the physical world we store our cash directly in our wallets, in the electronic world we have digital wallets. Digital wallets are where all the Bitcoin transaction nodes reside, in all the digital wallets of the all cryptocurrency holders in all the world simultaneously.

How can find a stored transaction?

The record, or ledger of these transactions  is known as the blockchain. You can access the public blockchain by entering a bitcoin address, transaction hash, or block number in a search bar of a site that has utilized open source Bitcoin Developer APIs  that enable search tools. A couple examples are blockexplorer.com and blockchain.info