Ейный: hers; slang and folksy
Way back in Russian 101, first we mastered the personal pronouns like мы (we), он (he) and они (they) and got through the shock of two forms of "you" (вы and ты).
Then we learned the possessive pronouns that matched them, like их (their) and его (his). Here we had another shock — свой, the possessive pronoun used with every pronoun to refer to his/her/their/our own something or other. But endless role-playing got us through я потеряла свой ключ (I lost my key) and он взял его шляпу (he took the other guy's hat).
And then came shock number three. We discovered a whole other set of possessive pronouns, some considered regional, slangy or so sub-standard that they aren't included in many dictionaries. Maybe we can't use them without sounding like weird hicks, but lots of our friends and neighbors use them to great effect.
For example, along with наш (our), you might hear нашенский (sometimes spelled нашинский). Нашенский is наш with a folksy twist, or with affection, or with a bit of irony. Sometimes it means "belonging to us": Дальний Восток хоть и нашенский, но очень уж он далеко (The Far East might be ours, but it's really very far away). Often it means "like us": Я же говорил — нашенский он! (I told you he's one of us!) Sometimes it means "in our language": Говори по-нашенски! (Speak in plain old Russian!)
Нашенский is often juxtaposed against ихний, a great word that gives the possessive pronoun их (their) a familiar adjectival form. Всё-таки есть две ментальности — нашенская и ихняя (In the end, there are two mentalities — ours and theirs). In the village, ихний can be a neutral word: Ихний дом сгорел (Their house burned down). But when the word refers to foreigners, there is often a touch of condescension, like in this funny exchange: Как там ихний журнал называется? «Упс»? — «Форбс». ("What's the name of that foreign magazine? 'Oops?'" "Forbes.")
По-ихнему can mean "according to them": По-ихнему, я просто негодяй (They think I'm a rat.) Or it can mean "the way they do something" — "they" usually being foreigners: Менеджер сказал, что будем работать по-ихнему (The manager said that we were going to work foreign-style.) Or it can mean "in their language": Когда ты научился говорить по-ихнему? (When did you learn to speak their language?)
The possessive pronouns его and её also have longer, folksy forms — евойный and ейный respectively — although they don't seem to be used as frequently as ихний. But you might read or hear: Мне бы ейные заботы. (I should have her problems.) Or: Евойный папаша и моя бабушка — давние знакомые (His pa and my grandma are old friends).
Свойский isn't really a folksy version of свой, but has its own meanings. Свойский can mean someone who is friendly and outgoing: Шофёр попался свойский, и минут через десять я уже знал всё о здешних политиках. (The driver turned out to be chatty, and in about 10 minutes I already knew everything there was to know about the local politicians.) A bit less commonly it can mean "not store-bought": Хлеб — свойский (The bread is home-made). The adverb свойски suggests an action that is very informal, without ceremony. Он свойски сел к компьютеру и быстро написал текст (He made himself at home at the computer and quickly banged out a text).
То есть, не по-ихнему (That is, not like them foreigners).