I'm not entirely sure but I think I read somewhere because "svært" is an adverb (of degree) here qualifying the amount of hunger the kids have. I couldn't find the grammar rules but I think most adverbs have one form only, in this case "svært". Somebody please correct me if I'm wrong here!! ;)
You are right. "svært" is an adverb, it describes the adjective "sultne". And you are also right about adverbs having only one form, they do not have different forms for gender and number. Diego is right too, the adverb corresponding to an adjective is the same as the adjective in neuter singular.
For anyone who would like to know more about svær's etymology and relationship to other Germanic languages. It is cognate with English 'sweer': https://en.m.wiktionary.org/wiki/Reconstruction:Proto-Germanic/swēraz
In the dictionary it ia said that svært is an adjective and not an adverb: https://ordbok.uib.no/perl/ordbok.cgi?OPP=Svært&ant_bokmaal=5&ant_nynorsk=5&bokmaal=+&ordbok=bokmaal Since that is the case, why is it not in its plural form 'svære'? Thanks in advance!