I’ll try and answer as best I can. Information on the various types of travelcard is one thing I must add at some point, and odd-period versions is high on the list.
In terms of the cost you can make a rough calculation as follows: Divide the monthly price by 30 to get the daily add-on and then multiply that by the number of odd days beyond whole months. Add on the monthly rate for each whole month and that is roughly the price of the ticket. The whole months run from the date it starts to the day before the monthly anniversary (eg 15th-14th). This does mean that the price for a 44 day season will vary depending on how many days are in the month that it starts in. A zone 2-4 monthly travelcard is £117.90 and the rough daily add-on is £3.93. If you start on July 15th then the month takes you to August 14th (31 days) and you need 13 extra days so that is £51.09. Add on the monthly and you get £168.99. The official calculation is a little more complex using multiples of 5 extra days plus odd days above that, and the result is rounded to a multiple of 10p, but £169.00 is likely to be close.
The situation regarding where to purchase is sadly becoming quite restricted. The ticket system required to add travelcards to an Oyster card is gradually being phased out at National Rail stations. I’m trying to get a grasp of the current situation at the moment. Ticket machines will only sell fixed period tickets, so there are only two reliable sources left: Heathrow, King’s Cross, Liverpool Street, Piccadilly Circus and Victoria Visitor Centres; and online.
Online has been known to be problematic for overseas residents in the past, but I’ve just checked again and the address entry does now allow you to select a country. If you can set up an online account and add your Oyster card to it then you can order odd-period travelcards which will be downloaded to your card when you use it within 3 days of ordering.