Svär- is the prefix for in-laws. It used to be a word on its own in Old Swedish meaning ’father-in-law’, related to Latin ’socer’ (father-in-law), but now it’s just a prefix. It’s related to svåger ’brother-in-law’ and svägerska ’sister-in-law’. Other words with this include: svärson ’son-in-law’, svärmor ’mother-in-law’, svärfar ’father-in-law’.
You have related words in the other Germanic languages like sviger- in Danish/Norwegian and Schwieger- in German, sweor in Old English meaning ’father-in-law’.
"Stödja" and "stöda" is variants of the same word, but "stötta" is a different word. They are very similar in use and meaning though, both typically translared to "support", as verb.
In a word frequenzy list, "stödja" was more common, which is the likely reason for only that being in your dictionary.
When "support" is used as a noun, "stöd" is more general and common, "stötta" more specific and not used figuratively. (Even "stödja" can apparently be a noun, but I have never seen that used that way.)