Bitcoin has a complex scripting system which can be used to set the conditions under which the money sent by a transaction can be redeemed. For example, it is possible to send bitcoins in such a way that they can be only redeemed by someone who finds a collision for a specific hash function.
Most of the time, however, bitcoins are sent to a script which requires a signature from a single key to redeem. In this case, the address is the encoded hash of that key. In general, however, not every script corresponds to an address.
Strange transactions are transactions which have either input or output scripts not matching any of the predefined patterns for standard scripts. Such transactions must be created manually, but they can contain any script permitted by Bitcoin. So, there are no specific patterns that they follow, but rather there are patterns that they do not follow.