The data for the discussion below appears in a pdf file that I uploaded to a pdf hosting site.The pdf document was created from an Excel spreadsheeet. It lists the Irregular Openings twice. On page 1 they are listed in conventional sequence and on page 2 they are sorted according to changes in positional value due to the opening moves. Here is the link.
I evaluated the irregular openings using engine analysis and compared them by computing the net gain to black, or in other words, the net loss in white's position, in playing the opening.
I computed black's gain by subtracting the engine's evaluation of white's position at the end of the opening from the value of white's position at the start of the game. The numerical value of the position is measured on a scale in which the material value of a pawn is set to 100 points. At the start of the game, white has an advantage - usually between 15 and 22 points according to which engine you are using - by virtue of holding the first move. In my case this value was set at 20 points. So for example if after a given opening is played out the value of white position increases to 50, then black's gain is 20 - 50 or -30 points. If instead, the value of white position changes to 10 points, then black gains 20 - 10 or +10 points - and so on.
What I found in the irregular openings is that mostly black wins in terms of positional evaluation. Using the numerical value of black's gain as a metric, we can divide the A00 Irregular Openings into three groups marked as X, Y, and Z and colored red, blue, and green in page 2 of the pdf document.
In the X-group - written in red letters - are openings in which black appears to lose positional value. So it appears that white has gained an unusual advantage by playing an irregular opening - but that only works if black plays the assumed book move in reply to white's irregular opening move. In fact these assumed moves are sub optimal and are not likely to be played. When black's move is corrected according to what I show in the data as the "best" continuation, white's illusory gain disappears.
In the Y-group - colored blue - are openings that are rather harmless to white except for the fact that white has given away all or part of its first move advantage to black. It is interesting to analyze these openings in reverse by imagining that black is playing the first move. One can then see the inverse form of more conventional openings such as the Sicilian.
The Z-group of irregular openings marked in green are losers for white because they result in a clear win in positional value for black. These openings are likely to have been refuted by the masters of chess and probably should never be played.
The Dunst Opening is noteworthy in that it is used by the engines when they play without an opening book but it is rarely seen in human matches or in engine matches played with opening books.