You cannot deposit USD, EUR, etc directly into Coinomi. You can buy crypto currency with fiat currency directly from Coinomi via third party services. To buy coins, simply open the left side menu and select an option from the "Buy crypto" section. Coinomi doesn't hold any fiat currency. All assets controlled by Coinomi are crypto assets, that may or may not have a monetary value.
You cannot withdraw fiat currency directly from Coinomi. To withdraw any cryptocurrency to your bank account, you should first open an account in a crypto-exchange that works with your bank, and transfer your coins to be sold there. Another option is to trade with cryptocurrencies directly, by exchanging them for goods or services with merchants that accept them.
If you already have a supported cryptocurrency in Coinomi, you can exchange it to another. Simply open the left-hand side menu and select one of our listed integrated exchanges.