Call Apple

When all the 'normal' (http://support.apple.com/kb/HT5787) verifications do not work, how can the iCloud be certain it is you?

You can call/contact Apple (http://support.apple.com/kb/HT5699). They will try to validate your account by multiple other ways. (billing information, creditcard info, etc). And one of the things they will probably ask for is some email conversations with other persons. So you might need to contact some friends/family/colleagues to dig in there archive for email conversations with your iCloud account.

You might expect your Apple contact to be suspicious, as they have recently had troubles with 'hacked' (wiki link) iCloud accounts.

Might this be a good lesson to always have a valid backup email address and a working 2-step verification☝️.

While I can assume that you ask due to having forgotten the password, it is not clear from your question.

In case you still know the password, you can log on to the iCloud account at appleid.apple.com, change the e-mail address and make it the primary e-mail address.

NOTE: Obviously, you cannot use an e-mail address you already associated with an Apple ID in a different account.