I am an eager learner and would love the chance to shadow someone on the weekends as they look for deals, and would be open to helping out with any work, such as cold calling, knocking on doors, etc... 

To save cash, start with a specific market or neighborhood and work it in all the ways you've read about (mail, calls, door knocking, etc).

Keep in mind the ones that are selling for crazy amounts of money are the ones on the MLS, you can always find off market deals through word of mouth, direct mail, door knocking, etc.

Knock on doors.

Your a Realtor ever think about door knocking to get listings and wholesale? 

The owner received a " fat check". and is on a time crutch to either knock it down andremove it . 

I was thinking of either mailing the owner directly or knocking on the neighbor’s door to see if they know anything and have any sort of contact.

Just knocking on a neighbors door can land you a deal.

Needless to say, after closing I was working on the property when I heard a knock on the door.

As for off market, try driving for dollars, direct mail marketing, skip tracing phone numbers and cold calling, door knocking, anything you can think of to get in contact with owners and seeing if they'll consider selling.