Rabbi Ahron Marcus brought the meanings of most of the names in Ancient Persian (Barzilai, pg. 321):
Dalfon - the proud
Aspata - the soldier
Porata - the elder
Adalya - the brave
Aridata - a creature/creation of the lord
Parmashta - a title for a high-ranking person
Arisai - the shadow of an Aryan
Vaizata - a creation of "the great one" (=Ahura Mazda)
The meanings of Parshandata and Aridai were unknown to him. However, presumably they went along with the themes of the rest of the sons' names, which are: Strong Persian heritage1 and a feeling of superiority, which go well with the character of Haman as presented in Esther.
1 Recently I saw an idea by Prof. Yehoshua Grintz (מוצאי דורות, pg. 95-96; can also be found on JSTOR) that when examining etymological, Tanachic and archeological information, it seems quite possible that the Amalekites were not descendants of Esav but descendants of Elam, AKA Persia. One point of evidence is that the names Amalek and Agag have Elamite characteristics and not Semitic ones, as one would expect from a descendant of the Semitic Esav (the Edomite language was a Hebrew dialect). That Esav had a son named Amalek does not necessarily prove they're his descendants because many of the descendants of Avraham shared names with other ethnic groups or had names that originated in foreign languages.