Sorry you have had to wait so long for an answer. I don't think mine is going to be very helpful, but it's a start. I'll answer the second question first, as the answer affects the first.
2. Yes, the lack of degree will affect your chances of getting a visa in some countries. You must check this before you jet off anywhere, or you may find that you have wasted an air fare.
1. The answer to this is very personal. There is no doubt that in some places arriving in a city and doing the rounds will land you a job. It's a good idea to have a carefully prepared c.v./resume to leave at each school. It helps if you can find out the name of the Director of Studies or person responsible for recruiting so that you can write your covering letter to a named peson, and put his/her name on the envelope you leave.
When you arrive at a school to drop off your application, be clean, sober, and reasonably dressed. The person you see at the desk may be the person responsible for recruiting, and first impressions are important. Be prepared. There is just an off-chance that you may be asked if you are available for interview on the spot. It's unlikely, but you don't want to miss any chance.
Whether or not you actually do try to find work in person depends a lot on your financial resources and time constraints. Can you afford to spend a couple of weeks or more in the foreign city while you are looking? Have you got the fare home if you are unsuccessful?
If you apply from home, you can send off several email applications in the time it takes you to visit one school - and you can send to several countries unless you have fixed on one.
So, there are some starting points.
- For Teachers