Illya and Wye
Illya doesn't tend to interact with Mr. Wye very often. His grievance is with Mr. Ecks. And, since Ecks is alive, Wye doesn't care much to associate with Illya. If they are all speaking as a group, however, they will exchange words. And now that Illya has saved Ecks' life, Wye certainly feels better about him than he did.
Napoleon and Ecks
Napoleon and Ecks rarely interact, either, except in cases of group conversations. Napoleon did try to perform artificial respiration and CPR on him when he was laying dead from rescuing Napoleon from being shot with a blaster gun.
Wye and Mr. Waverly
Wye met Mr. Waverly in London, following the main fall of the extremist organization. Mr. Waverly was inspecting the remains of the organization's buildings, including Mr. Zed's house. Wye was investigating as well, wanting to make sure the organization would not pose a major threat to him and Ecks. He had just been released from the hospital and was on his way to find out whether Ecks was still among the living. Upon meeting Mr. Waverly, they shared a deep and mature conversation, during which Mr. Waverly came to realize who Wye was.
In the end Mr. Waverly let him go. He was listed as Deceased in U.N.C.L.E.'s files and hence, there was no warrant out on him. In addition, Mr. Waverly felt that he was no longer a threat to world stability since his only desire was to find Ecks and start over fresh elsewhere, allowing Ecks the freedom he had longed for all of his life. Mr. Waverly, then, became aware of Wye's survival before Napoleon and Illya did, although he didn't know for sure that Ecks had survived as well. But he said nothing, preferring to continue to list Wye and Ecks as Deceased in U.N.C.L.E.'s files. Since Ecks and Wye were codenamed agents for an organization that was now officially defunct, he felt that technically, the Deceased status still stood.
Wye respects Mr. Waverly, both as a leader and because Mr. Waverly had the compassion and insight to allow him to slip away. Mr. Waverly, although not approving of or understanding Wye's life choices in the past, appreciates the man's love for his partner and friend and his desire to give Ecks the free life he's longed for.
They keep up the ruse of not knowing each other and introduce themselves to each other at the end of The Peaceful Meadows Affair. Perhaps the truth will be known to Napoleon and Illya someday or perhaps not.