Something cool happened...I found out what these glasses were.
More than a year ago my dad found me the most beautiful amber lamp. Along with the lamp he found a set of four faceted amber goblets. Through a series of links from search results for amber glass, a similar glass to mine showed up on the screen, but in green.
This is how I found out that they are pressed glass tumblers manufactured by the Indiana Glass Company (1907-2002) of Dunkirk, IN . During the years between 1960 and the '80s, there were many similar looking patterns out there such as the Fostoria American, Indiana Glass American Whitehall (a much later style after they bought Fostoria) and the Jeanette Glass Co. Cube designs. However, I have been able to identify mine as Whitehall, just Whitehall, which were produced from the 1960s to the 1980s and came in gold (amber) olive (avocado), and crystal clear. Later in the run, designs were also available in a light blue and teal.
Here is a chart from the Indiana Glass factory that shows the other items that were part of this line. I'm thinking it sure would be nice to have a few of those avocado green and teal glasses in my cabinet too.
The best thing, is that these are still plentiful at thrift stores and online and are quite affordable at $6-$8 per glass or $22 for a pitcher.