Kaji and Shinji (Relationship)
Shinji looks up to Kaji as a sort of mentor, and accepts behavior in him that he would disapprove of in other characters. For instance, in Episode 08 when Kaji asks him about Misato's sleeping habits, implying that Shinji and Misato might be in a sexual relationship and simultaneously implying that he is intimately familiar with these habits as well, Shinji just laughs. If anyone else asked him that same question he would probably have stuttered with embarrassment, barely able to get out a denial. After the Israfel fiasco, it was Kaji who came up with the idea of the dance routine to help Shinji and Asuka synchronize with each other. His relationship with Misato is constantly paralleled with Shinji's own relationship with Asuka, as he is a sort of role model and relatively positive adult version of Shinji. Kaji gives advice to Shinji multiple times on many matters though Shinji has difficulty understanding him, as Kaji has his own insecurities. He motivates Shinji to pilot again in Episode 19.
However, Kaji's own feelings regarding Shinji are unclear at best and generally never talked about, much like Kaji's feelings regarding anyone. It might be also worth noting that Shinji didn't seem to express aproval at Kaji's cynical view of the unavoidable distance regarding the relationship between men and women.