Here's a pretty comprehensive bibliography of articles and chapters relating specifically to the epistle of Third John. If I've missed anything, please let me know.
Campbell, Barth L. “Honor, hospitality and haughtiness: the
contention for leadership in 3 John.” EQ
77 (2005): 321-341.
Clark, David J. “Discourse Structure in 3 John,” BT 57 (2006): 109 – 15.
Donfried, Karl P. “Ecclesiastical Authority in 2-3 John,” Évangile de Jean: Sources, rédaction, théologie. Edited by M. de Jonge. BETL44
(Gembloux: Duculot, 1977), 325-333.
Floor, Sebastiaan “A Discourse Analysis of 3 John,” Notes on Translation 4.4 (1990): 1-17.
Funk, Robert W. “The Form and Structure of II and III John.”
Journal of Biblical Literature 86
(1967): 424-30.
Horvath, T. “3 Jn 11b: An Early Ecumenical Creed?” The Expository Times 85 (1974): 339-340.
Landrus, Heather L. “Hearing 3 John 2 in the Voices of
History,” Journal of Pentecostal Theology
11.1 (2002): 70-88.
Lorencin, Igor “Hospitality versus Patronage: An
Investigation of Social Dynamics in the Third Epistle of John” Andrews University Seminary Studies 46.2
(2008): 165-174.
Malherbe, A. J. “Hospitality and Inhospitality in the
Church,” Social Aspects of Early
Christianity (Philadelphia: Fortress, 1983), 92-112.
Malina, B. J. “The Received View and What it Cannot Do: III
John and Hospitality,” Semeia ():
171-194.
Mitchell, Margaret M. “’Diotrephes Does Not Receive Us’: The
Lexicographical and Social Context of 3 John 9-10,” Journal of Biblical Literature 117.2 (1998): 299-320.
Neufeld, D., ‘The socio-rhetorical force of ‘truth talk’ and
lies: The case of 1 John’, HTS Theological Studies 67 (2011): 1-10.
O’Donnell, M.B., and C.J. Smith, ‘A Discourse Analysis of 3
John’ The Linguist as Pedagogue: Trends
in the Teaching and Linguistic Analysis of the Greek New Testament, Eds. S.E.
Porter and M.B. O’Donnell. (Sheffield: Sheffield Phoenix Press, 2009).
Polhill, John B. “An Analysis of II and III John.” Review & Expositor 67 (1970):
461-471.
Polhill, John B. “The Setting of 2 John and 3 John,” Southern Baptist Journal of Theology
10.3 (2006): 28-39.
Storm, Melvin R. “Diotrephes: A Study of Rivalry in the
Apostolic Church”, ResQ 35 (1993):
193-202.
Van Oudtshoorn, A. “Every Letter Tells a Story: Mission and
Unity at Odds in the Local Church: A Socio-Narrative Analysis of 3 John,” Pacifica: Journal of the Melbourne College
of Divinity (2011): 267-282.
Watson, D. F. “A Rhetorical Analysis of 3 John: A Study in
Epistolary Rhetoric,” CBQ 51 (1989): 479-501.
Whitman, Andrew. “Third John: Helping or Hindering with the
Spread of the Gospel?” Evangel 15
(1997): 37-42.
