With respect to F. Scott Fitzgerald's The Great Gatsby, there are conflicts of all the types mentioned in the question with the major conflict involving Jay Gatsby's attempt to regain the love of Daisy Buchanan, a woman that he has idealized in his search for the idyllic and illusive American Dream.

Physical conflicts

While there is a physical tension between Tom and Gatsby when Gatsby asks Daisy to tell her husband that she does not love him, they do not come to blows.  However, Tom certainly abuses Myrtle physically, striking her full in the nose when she says the name of his wife in the hotel in New York.  In this display of brute force, Tom lets Myrtle know that she is still not worthy of his home or social class.

Psychological conflicts

Nick has internal conflicts as he perceives the decadent life in New York with its dishonest Jordan Baker and supercilious Tom Buchanan and frivolous and superficial guests at Gatsby's parties.  Certainly, he does not wish to involve himself with the clandestine meeting of Gatsby and Daisy.  There is no place for Nick because he is honest.

Jay Gatsby tries to be someone that he is not and has trouble maintaining his facade.  His attempts to attain the social status that he feels necessary to win Daisy finds him frustrated and almost desperate after the death of Myrtle Wilson. 

Social conflicts

The social disparity between West Egg and East Egg threads throughout the narrative of The Great Gatsby. Despite his cruelty and villainy, Tom Buchanan remains socially superior to Gatsby simply because of his family name and money. Of course, Gatsby's connections to Meyer Wolfscheim pose conflicts for Gatsy's social mobility from West Egg.  Nevertheless, true to his dream, he remains more decent that the immoral and materialistic East Egg, later becoming the sacrificial victim to this immorality as Daisy abandons him in her struggle to escape complicity in the murder of Myrtle Wilson.