Definitely, for multi-day trips the best is a Route-per-day (or Track if you prefer, or both).
On these Etrex GPSs, it's OK to have all your Routes and Tracks and Waypoints combined in a single GPX file.** Or they can be in separate files, or any combination, it really doesn't matter. The problem with lots of separate files is avoiding data anomalies where waypoint names are duplicated for example - these can easily occur but not generate much of a useful error message. A single file automatically avoids all this. They can be placed on the mSD card, or on the GPS memory, or any combination, again it doesn't matter. I prefer to use the mSD card and avoid touching the GPS memory where possible.
** NB some other Garmins can't do this, but with the Etrex 20 it's OK.
I'm not sure what you mean by 'file size'. I regularly load 2-week or 3-week trips in a single GPX file containing a Route per day.
There are well-known limits on numbers of points per Route, per Track, and in total, but they are pretty high and easily cover a month's cycling, let alone a few days.
If you want your GPS to 'follow road' a Route (autorouting) then there is a limit of 50 points in a Route. More than this simply won't compute. This may be what happened on your Ireland Route.
You can store up to 50 Routes however, and it's easy enough to switch from one to the next, on the road. Especially if you take care to name them sequentially.
You can also store up to 200 (I think) Tracks of up to 10,000 points each.
If you don't autoroute, then your Routes will work with up to 250 points. This is how I like to operate.
However you probably can't load 50 Routes all of 250 points, there will be an overall points limit but it's undocumented (for this model) as far as I know - at least 8,000 points and probably more.
But I find it's very rare to need more than 100 points in a day, and often far fewer. So 8,000 points is 80 days-worth.