The short answer is: in whatever order you like! But some folks like a little more guidance, so here’s some advice on this score.
Seasons one and two of Night Terrace happen in episode order, so those are easy: listen to episodes one through eight of season one, then one through eight of season two.
Hello! My Name is Eddie is set before the very first episode, “Moving House”. The episodes don’t reference each other, but there are some little references and one potential spoiler for season one, so for a first listen you should probably listen to it after season one.
The episodes of Horatio’s Travels sort of occur during the season two episode “The Retirement of Horatio Gray”. (It’s all quite timey-wimey, to steal a phrase.) You should probably listen to it after the end of season two, or at least after “The Retirement of Horatio Gray”.
“Situational Awareness“, the Night Your Own Terrace stories and the Bodgy Creek Community Podcast crossover “The Bodgy Files” aren’t set at a particular point in the continuity, but it makes the most sense for them to occur after the season one finale “Home”, and then either before the season two episode “Ancient History”, or after the season two finale “Home Again”. We do think “Situational Awareness” is a great way to end a re-listen of the current Night Terrace slate, though, so we’d suggest saving it until last.