This and the number of connectivity isomers of the other formulae have been determined by the remarkable computer program MOLGEN, developed by T. Grüner, A. Kerber, R. Laue, and A. Ruckdeschel, University of Bayreuth. The actual version is MOLGEN 4.0.
I have added one isomer for HNO3 which MOLGEN does not produce: It is the protonated complex NO3(-) with a 4-bonding N-atom at its center and a formal positive charge, the usual formula for HNO3, but, perhaps, not a compound within the class of "organic chemistry"? What about nitrobenzene, then? There is definitely no O-O bond in the stable groundstate molecule HNO3 nor in the nitro-group of nitrobenzene!
There are other, similar, cases: E.g. CH2N2 generates four Lewis-formulae among which H2C-NN, diazomethane, is missing. However, MOLGEN produces a graph with CH2 in a three ring structure with an N=N edge, a feature which has been disproved more than 40 years ago (by K. Clusius and coworkers) for groundstate diazomethane by isotope substitution, where the two N-atoms come out as being distinguishable and the graph of CNN linear.- The reason of the apparent failures of MOLGEN is simply that the rules within it restrict N to being 3-bonding and C 4-bonding. In HNO3 N is 4-bonding as in NH4(+) and in diazomethane C is 3-bonding with negative formal charge as in CH3(-). MOLGEN does not know about "formal" charges, often necessary to reconcile connectivity formulae with experimental structure information.
MOLGEN otherwise determines the number of connectivity isomers exhaustively and uniquely, i.e. without redundancy, applying the rules of 'organic chemistry' which is just Lewis+Senior!

For C2N2O most of the above formulae, except perhaps Nr. 19, NºC¾N=C=O, cyanogen-cyanatogen and Nr. 20, NºC¾O¾CºN, cyanogen-oxide O(CN)2 (S(CN)2 exists), would be predicted as unstable by most chemists, applying some variants of Bredt's rule, or rules about strained rings and "impossible" bond angles. As far as the collection of some 16000 organic compounds in the CRC-"Rubber Handbook" is representative, there is no compound C2N2O listed. However, Beilstein knows three stable C2N2O isomers.

Professor A. Kerber, Bayreuth, has kindly informed me about the last fact (I was too lazy to go to the library and lookup Beilstein!) as well as about a much wider range of accessible isomer classes offered by the full MOLGEN program. The on-line version, which I used above, is restricted to the 'normal' bond numbers (valencies). In the fully installed version you can define your own atom types, e.g. 'Np 4' (N positive, 4-bonding) and 'Cm 3' (C minus, 3-bonding) with which the difficulties with HNO3, CH2-NºN, and others can be resolved. It turns out that MOLGEN and its companion programs is the most comprehensive tool ever invented to derive isomer manifolds.
Here is what one obtains with "Cm1 3H2Np1 4N1" as input to the installed MOLGEN 3.5:



Nr. 4 is the traditional formula for diazomethane (it is linear, of course, Molgen does not show equilibrium structures). The numbers in kcal/mol are the standard formation enthalpies at 298 K, computed with the G3 combination of methods, as offered by Gaussian98/03. Cyanamide NH2CN is the most stable of these CH2N2 isomers.