Let's see if I can type them phonetically. Milngavie is pronounced MULGAYE - for the AYE think of the scots word for yes - aye.
Strathaven is pronounced STRAVEN.
There is, of course, a complete Glasgow vocabulary with many special local words for common things. Words like WAINS, GREETIN, SCUNNERED, SITOOTERY, BRAW to mention a few.
I'm from south London but have lived here for 39 years. When I first came up I struggled with understanding some of my new work colleagues, but you get used to it. What really surprised me was that they had trouble understanding me, and yet they hear southern English voices on the TV all the time. Odd.
The most difficult in my opinion is the NE Scottish, eg. Aberdeen & Peterhead. It's like Jordie but with a Scots accent and can be very hard to understand. Once you are into the true Highlands the accent is much softer and easy to get along with.