Someone who loves to read is called a "bookworm". Usually people use "geek" and "nerd" to mean the same thing. I found this online: Geek - An enthusiast of a particular topic or field. Geeks are “collection” oriented, gathering facts and mementos related to their subject of interest. They are obsessed with the newest, coolest, trendiest things that their subject has to offer. Nerd - A studious intellectual, although again of a particular topic or field. Nerds are “achievement” oriented, and focus their efforts on acquiring knowledge and skill over trivia and memorabilia.

"has a mind like a sponge"

There are so many words but depends on whether it is positive or negative. bookworm, geek, nerd has negative connotations. savant, scholarly, intellect, learned, erudite, etc has positive nuances. Of course, depending on how your tone and intentions, it can be become positive or negative. "You silly little geek of mine", the mother said to her son. Now "geek" takes on a positive and loving meaning.

A person who loves studying and has accumulated a lot of knowledge from their study can be described as erudite.

For a word with a positive connotation you could use ‘studious’ or ‘intellectual’, or a phrase like ‘he is fond of intellectual pursuits’. ‘Nerd’ is sort of positive and sort of not, I mean it started as an insult but has been ‘owned’ by nerds as a badge of their ‘nerdiness’ - in a positive way. Geek has the more specific meaning of someone who is really into a particular thing or things, like someone who is really into Star Wars trivia, for example, or who knows all kinds of unusual information about coffee, or whatever.