na-adjective, noun which may take the genitive case particle 'no'
various; a variety of; all sorts of
Describes a range of different things, people, or situations. Used as a na-adjective or with の to modify nouns.
This shop has various kinds of bread.
I want to travel to various countries.
adverb, adverb taking the 'to' particle
variously; in various ways
Adverbial use describing actions done in many different ways or with variety. Often used with と.
He thought about the problem in various ways.
Thank you for all your help (in many ways).
Noun usage, often in the pattern 〜のいろいろ to mean 'various things about...' or 'the various aspects of...'. Can also stand alone.
I experienced various things in life.
I have various things I want to talk about today.
The shop has all sorts of products lined up.
He looked into it in various ways before deciding.
We talked about the various aspects of child-rearing.
Thank you for all your help over the past year.
色々 is a general, neutral word for 'various', whereas まちまち adds a nuance of things being scattered or not aligned.
色々 stresses variety ('various kinds'), while 数々 stresses a large quantity, often of noteworthy things.
色々 emphasizes variety or diversity among things, while あらゆる emphasizes exhaustiveness, covering every single instance without exception.
色々 is a general word for 'various' usable as noun or adverb, while 何かと specifically stresses multiple unspecified ways or reasons for something happening.
いろいろ simply means 'various' and can describe things or actions broadly, whereas そんなこんな specifically refers back to a jumble of prior happenings, often as そんなこんなで.