Words can carry meanings in two different ways: connotative and denotative. The denotation of a word is the meaning that you will find next to the word in the dictionary. The connotations of a word are the feelings or thoughts that the words suggest, that they remind you of, even if they do not denote it directly. For example, "short", "stumpy", "dwarfish" are all different ways of describing someone who is the opposite of tall. However, each of these words is only appropriate in certain contexts as they have different connotations. Some would be seen as quite rude when used to describe someone in person. The connotations of a word are incredibly important for determining its meanings and should be attended to with care.
As another example here are a few different words for food: "grub", "scoff", "nourishment". The first two words "grub" and "scoff" are old-fashioned slang words for food in British English. They would only be used in a very informal context and usually only in the United Kingdom or certain commonwealth countries. This is part of their connotative meaning. You would never call a very expensive meal "scoff" unless as a joke and then only in the company of certain people. "Nourishment" meanwhile is a highly formal word and would rarely be spoken except in a scientific or academic context. Their denotative meanings may be the same but their connotations are completely different.
So, if we can learn the denotative meaning of a word from its dictionary definition how do we learn a word's connotations? Unfortunately, although it is simple to understand what a connotation is, learning the connotations of words is one of the most difficult and time-consuming aspects of learning a language. A word's connotations generally come from the company they keep. You can figure out the connotations of a word by looking at the kinds of books or conversations you normally find it in and the other words that it normally comes along with. Many words have a scientific context, for instance, because they are only ever found in scientific textbooks.
Formal and informal are two major types of connotation and, again, there is no easy way to learn the difference between formal and informal words other than to observe the contexts in which they appear. Informal words are likely to be found in conversations between close friends whereas formal words are more likely to be found in books or in exceptionally polite conversations.
It would be impossible for us to provide a list of connotative words because almost all non-grammatical words could be said to have connotations, just as almost all words have definitions. However, some words tend to have stronger connotations than others. "Tall", for instance, is a fairly neutral word to describe someone who is over average height. It is neither formal nor informal, scientific nor colloquial. It can, moreover, be used in a wide variety of contexts.