When Samson returned to check on the carcass of the lion he had slain, did he ceremonially defile himself (especially considering that he took honey from out of the carcass)? Would even the jawbone of an ass have made him unclean? Secondly, would his killing of the Philistines have been contrary to his Nazarite vow, if he came into contact with their bodies after he had killed them? Just trying to understand how this would have worked.
According to Nazir 4b, Samson, having a special form of nezirut (Nazirite status), was allowed to become tamei (ritually impure or "unclean") even though the typical nazirite vow would preclude such a leniency:
נזיר שמשון מותר ליטמא למתים שכן מצינו בשמשון שנטמא
A nazir shimshon is allowed to become impure via [contact with] the dead, for we find by Samson that he became impure.
The Talmud there also points out that indeed Samson himself never made nazirite vow. Regardless, even for a typical nazir, the prohibition on becoming impure is solely with regard to the impurity of deceased humans, not animal remains.
Samson was not a nazirite in a complete sense, for he never took a nazirite vow.It was merely that the angel caused him to be separated from impurity.
What were the laws applying to him? He was forbidden to drink wine and cut his hair. He was, however, permitted to incur impurity due to contact with the dead. This concept is a halachah transmitted by the Oral Tradition.
Rambam, Hilkhoth Naziruth Halakha 3:13
Touching a carcass of an animal although it may render a Nozir impure it is permitted and would not render his nezirus invalid source is Pesachim 80b:
טומאת התהום דשרץ ובמאי עסקינן אי נימא בבעלים ובמאן אי בנזיר מי מהני ביה (במדבר ו, כי ימות מת עליו אמר רחמנא (Bamidbar 6,9) - unknown Tuma of touching a sheretz (or a neveila) if we are dealing with a case of Nazir is it forbiddon? Surely not Because it state "if a dead man dies with him" i.e only a dead man invalidates his nezirus.
Your second question about killing the philistines with the jawbone of the animal the gemoro nazir 4b adresses your question:
ומנלן דאיטמי למתים אילימא מדכתיב (שופטים טו,טז) בלחי החמור הכיתי אלף איש דילמא גרויי גרי בהו ולא נגע בהו And from where do we derive that Samson became impure from corpses? If we say it is from the fact that it is written: “And Samson said: With the jawbone of an ass, I smote a thousand men” (Judges 15:16), perhaps he thrust the jawbone at them but did not touch them, and he remained pure.
אלא מהכא (שופטים יד, יט) ויך מהם שלשים איש ויקח את חליצותם דילמא אשלחינון ברישא והדר קטלינן ויך ויקח כתיב Rather, it is derived from here: “And he smote thirty men of them, and took their garments” (Judges 14:19). Since he stripped the clothes off the dead he must have come into contact with them. The Gemara counters: Perhaps he stripped them first and afterward killed them. The Gemara responds: It is written: “And he smote…and took,” in that order, indicating that first he killed them and then he took their clothing.
ודילמא גוססין שוינן אלא גמרא גמירי לה But perhaps he mortally wounded them and thereby caused them to be in the process of dying, and he then took their clothes before they died so that he would not touch their corpses. Rather, it must be concluded that it is learned as a tradition that Samson wa allowed become impure from corpses even though there is no proof from scripture.
So we see there is no proof Shimshon violated any form of nezirus but at the same time oral tradition dictates that his special Nezirus called "nazir Shimshon" would be permitted to come in contact with dead bodies and only prohibited to cut his hair or drink wine (or eat grapes)