I would say that it is probably grammatical, but because 'neither' is not common introducing a clause like that, it is very confusing: it is not clear on first reading what the relationship is between the main clause and the parenthetical phrase.
Apart from the suggestions already made, 'but' would mend it, as it makes the relationship between them clearer: XXIII, but neither IIIXX nor XIIIX,
english.stackexchange.com/users/547/Colin Fine
I would say "The Roman numeral for 23 is XXIII.
Variations like IIIXXX and XIIIX, although logical, would not be correct."
english.stackexchange.com/users/1584/Mike Pope
I see no reason for it to be incorrect: 'neither IIIXX, nor XIIX' is known as dependent clause , so you have: (subject) (dependent clause) (transitive verb) (direct object) (adverbial phrase)
It is the same, in my opinion, as
In Roman, XXIII — not IIIXX or XIIX —
represents 23 Of course, adverbial phrases can be moved around reasonably freely.
However, I do like Mike Pope's rewording.
english.stackexchange.com/users/1065/J D OConal
I'm not sure if it's correct grammar, but it sounds awkward to me.
It's like saying he, neither she nor it, is going to the store.
It just doesn't sound right.
I would instead say: XXIII represents 23 in roman, but IIIXX and XIIIX do not.
english.stackexchange.com/users/1606/Claudiu
If you really want to use that construction, then "XXIII, not IIIXX or XIIIX, represents 23 in Roman numerals", but other respondents have suggested more elegant forms.
Incidentally
(and I know you didn't say this, but still...), neither IIIXX or XIIIX can represent 23, so I wouldn't say "although logical", as per Mike Pope's suggestion.
IIIXX and XIIIX would represent 17, although they both break the rules of Roman numeral syntax, I believe.
Also, "roman" should be capitalised: "Roman".
english.stackexchange.com/users/1402/gkrogers
I want to say that we cannot represent 23 in Roman as both IIIXX and XIIIX. The correct representation for 23 in Roman is XXIII.  If I write like this   XXIII, neither IIIXX nor XIIIX, represents 23 in roman.   is it correct grammar?
XXIII, neither IIIXX nor XIIIX, represents 23. Is it correct grammar?
english.stackexchange.com
<grammaticality><conjunctions><neither-nor>
english.stackexchange.com/questions/3959
english.stackexchange.com/users/1660/xport
It is generally agreed that, whilst this phrase might be correct grammar, it does not sound particularly natural, and in fact, might be a little confusing. There is divided opinion as to how the phrase should be written. Some people believe grammatically, the form is correct. However, a better way of phrasing suggested is "The The Roman numeral for 23 is XXIII." Others feel it sounds awkard, even if it supposed to be grammaticaly correct and suggest "XXIII represents 23 in roman, but IIIXX and XIIIX do not."  
It is generally agreed that, whilst this phrase might be correct grammar, it does not sound particularly natural, and in fact, might be a little confusing. It may be correct grammatically, but it sounds awkward. The best way to put it is: "The Roman numeral for 23 is XXIII and variations like IIIXXX and XIIIX, although logical, would not be correct."
There is no reason for it to be incorrect: 'neither IIIXX, nor XIIX' is known as  dependent clause , so you have:   (subject) (dependent clause) (transitive verb) (direct object) (adverbial phrase). However, although it is probably grammatical, as 'neither' is not common when introducing a clause like that, it is very confusing: it is not clear on first reading what the relationship is between the main clause and the parenthetical phrase. It is generally agreed that, whilst this phrase might be correct grammar, it does not sound particularly natural, and in fact, might be a little confusing.
Gramatically, it is correct. The sentence may be grammatically correct, but it sounds awkward.
It may be correct grammatically, but it sounds awkward. The best way to put it is: "The Roman numeral for 23 is XXIII and variations like IIIXXX and XIIIX, although logical, would not be correct."
It is generally agreed that, whilst this phrase might be correct grammar, it does not sound particularly natural, and in fact, might be a little confusing.