deep dive on the PJO/HoO characters and language:
percy: english, ancient greek, latin, spanish
annabeth: english, ancient greek, morse code
grover: english, zoolingualism
piper: english, ancient greek, french
leo: english, ancient greek, spanish, morse code
hazel: english, latin, french
frank: english, latin, french, mandarin
nico: english, italian, ancient greek
reyna: english, latin, spanish
despite the high majority of characters in both PJO and HoO being multilingual, leo, hazel, frank, reyna, percy, and nico are the only characters to actively learn multiple spoken languages. the rest only know another language due to their godly parents, and their other language(s) is intrinsic.
out of the seven, 4/7 have actively learned more than one spoken language. annabeth, piper, and jason are the exceptions.
almost every character who has learned multiple spoken languages has done so from youth. leo learned spanish from his mother, frank learned mandarin from his family and french because he's canadian, hazel learned french in school, reyna learned spanish because she's puerto rican, and nico learned italian because he's italian.
the only canon exception is percy, who is taking dual-credit spanish in school in senior year.
out of the characters who learned more than one spoken language, only frank speaks languages from different language families (english/french + mandarin).
frank, hazel, and percy are said to not be fluent in the non-english languages they have learned. leo, reyna, and nico are all fluent in their non-english (learned) language.
hazel, frank, and piper speak with different french dialects. hazel speaks in louisiana french, frank in canadian french, and piper most probably in standard french. it's confirmed hazel and frank have a hard time speaking to one another in french.
percy does speak to horses, but it's implied not to be because he "speaks their language", like grover who is not understood by percy when he communicates with animals. it's more like some sort of automatic translator in percy's brain. he understands horses because he hears them speak in english in his head. same applies to him with marine animals.
out of these characters, only two are shown to know nonspoken languages, with annabeth and leo both knowing morse code. this is widely different from Magnus Chase, where the majority know a fictional form of sign language called Alf sign language.
frank communicates in different animal languages based on the animal he transforms to, but in his standard human form, he does not show signs of zoolingualism like grover does.
characters with confirmed dialects/accents:
hazel: louisiana french, no specified english dialect/accent
frank: canadian french, no specified english/mandarin dialect/accent
leo: mexican spanish, no specified english/mandarin dialect/accent
reyna: puerto rican spanish, no specified english dialect/accent
it can be assumed most characters with intrinsic abilities to speak a language would speak the standard version of said language, but that has not been confirmed.