Vocabulary

Dictionaries

Merriam-Webster’s Learner’s Dictionary is my #1 recommendation.
Cambridge Learner’s Dictionary is also excellent, especially for British English.

The Academic Word List (AWL) contains 570 word families that are crucial for academic research and writing.
RMIT University has an excellent site with activities to practice the AWL words.

Collocations are words that are often used together. Learning collocations can help your speaking and writing sound more fluid and advanced.
OzDic.com is a great collocations dictionary. Just enter the word you are interested in, and you will find a list of collocations.
The Academic Collocation List is an excellent resource for academics and advanced students.

Phrasal verbs are verbs with one or two particles (usually prepositions). These multi-word verbs are VERY common in spoken and informal English, and can be hard to understand. Examples include: look up, break up with, work out, pass out, drop off, and many, MANY more.
Phrasal Verb Demon has many examples and useful exercises.
Perfect English Grammar (a great grammar website) has a large phrasal verb section too.

Idioms are phrases that are used in spoken and informal English and that are not literal. Collocations and phrasal verbs can be types of idioms. Idioms can also be more fun, such as a student saying “the quiz was a piece of cake” to mean that it was easy.
The Idioms Dictionary is a great place to start.
The Free Dictionary also has an Idioms section.
You may also want to Google “education idioms” or “medical idioms” or whatever field you are studying or interested in + “idioms.”