You do not need a WiFi connection to send or receive email, but the account must be set up correctly on the phone. If you set it to sync with Outlook and then synced the phone it should transfer your mail settings to the phone, but it doesn't always get them right, especially if your email provider requires different settings if you are connected to their network or on a public connection..
If you open the email app do you see the email account you use with Outlook?
Is the email account with an Exchange server (usually corporate), or with a POP3 or IMAP mail server (usually an ISP account).
If it's IMAP or POP3 and you are receiving email, then the problem is the Outgoing mail server settings on the phone (called "SMTP" settings). you should go to your ISP's web site to find out what SMTP settings to use when off-network.