A nominative conjoined object (NomConjObj for short) is, first of all, a NP which is coordinate in form (consisting of two or more conjoined NPs) and which serves as an object (a direct object or prepositional object). Then, at least one of the conjuncts is visibly nominative — that is, it is a 1st or 3rd person personal pronoun in its nominative form. (Other NPs show no visible evidence of their case.) Although many combinations are attested, only two seem to be really frequent:
NP and I [e.g., “to Kim and I”]
he/she and NP [e.g., “to he and Kim”]
(You will see that both serial position and person/number features are relevant.)
[Clearly, “nominative conjoined object” is an imperfect name, but it’s hard to imagine how to pack all the relevant information into a reasonably short name. And anyway, labels are not definitions.]
The full set of facts about pronoun case in English ranges over quite a bit of territory, including, most notably, AccConjSubjs, as in “Me and Kim went swimming”. The advice literature on the general topic is vast, and I won’t attempt to survey it here, though I point out that MWDEU has an excellent entry (between you and I) on NomConjObjs.
On to some references on NomConjObjs.
2005 bibliography on pronoun case in coordination, from Thomas Grano:
Angermeyer, Philipp S. & Singler, John V. 2003. The case for politeness: Pronoun variation in co-ordinate NPs in object position in English. Language Variation and Change 15.171-209.
Boyland, Joyce Tang. 2001. Hypercorrect case in English? Cognitive processes that account for pronoun usage. In Joan L. Bybee & Paul Hopper (eds.), Frequency and the emergence of linguistic structure, 383-404. Amsterdam: John Benjamins.
Emonds, Joseph. 1986. Grammatically deviant prestige constructions. In Michael Brame, Heles Contreras, & Frederick J. Newmeyer (eds.), A festschrift for Sol Saporta, 93-129. Seattle: Noit Amrofer Publishing Co.
Honey, John. 1995. A new rule for the Queen and I? English Today 11.4.3-8.
Householder, Fred W. 1987. Some facts about me and I. Language Research 23.2.163-84.
Hudson, Richard. 1995. Does English really have case? Journal of Linguistics 31.375-92.
Jacobsson, Bengt. 2003. Notes on pronominal case in English. Studia Neophilologica 75.21-31.
Parker, Frank, Kathryn Riley, & Charles Meyer. 1988. Case assignment and the ordering of constituents in coordinate constructions. American Speech 63.3.214-33.
Quattlebaum, Judith A. 1994. A study of case assignment in coordinate noun phrases. The Language Quarterly 32.3-4.131-47.
Quinn, Heidi. 2002. The distribution of pronoun case forms in English. Ph.D. diss., Univ. of Canterbury, NZ.
– 2005. The distribution of pronoun case forms in English. Amsterdam: Benjamins. (rev. of Quinn 2002)
Redfern, R. K. 1994. Is between you and I good English? PADS 78.187-93.
Rini, Joel. 2003. The origin of Spanish entre tú y yo “between you and me”: A typological parallel to English between you and I? Diachronica 20.1.139-65.
Sadock, Jerrold M. 2005. Optimal morphology. In Cemil Orhan Orgun & Peter Sells (eds.), Morphology and the web of grammar: Essays in memory of Steven G. Lapointe, 83-94. Stanford CA: CSLI.
Schwartz, Bonnie D. 1985. Case and conjunction. Southern California Occasional Papers in Linguistics 10.161-86.
Sobin, Nicholas. 1997. Agreement, default rules, and grammatical viruses. Linguistic Inquiry 28.2.318-43.
Tieken-Boon van Ostade, Ingrid. 1994. Standard and non-standard pronominal usage in English, with special reference to the eighteenth century. In Dieter Stein & Ingrid Tieken-Boon Ostade (eds.), Towards a standard English: 1600-1800, 217-42. Berlin: Mouton de Gruyter.
Wales, Katie. 1996. Between you and I: problems of case. In Katie Wales, Personal pronouns in present-day English, 85-109. Cambridge Univ. Press.
Grano, Thomas. 2006. “Me and her” meets “he and I”: Case, person, and linear ordering in English coordinated pronouns. Honors thesis in linguistics, Stanford Univ. Available on-line here.
Some postings on pronoun case on Language Log and my blog (especially recommended items are asterisked):
AZ, 12/28/04: Here comes the accusative (link)
AZ, 5/29/05: Case nuances (link)
*AZ, 8/7/05: Just between Dr. Language and I (link)
AZ, 9/5/05: Someone like me, someone such as myself (link)
AZ, 2/11/06: Whatever is not prohibited is permitted — not! (link)
*GP, 12/19/06: Does Julia Gillard know subjects from objects? (link)
AZ, 2/26/08: National (omigod) Grammar Day (link)
*AZBlog, 6/23/09, Sotomayoral NomConjObj (link)