My daughter Thalia is 20 months old and a lot of what you are describing is going on here too. She doesn't say "no" but that's cos she doesn't know the word. That's partly on purpose- we don't actually say "no" a lot- usually redirect to what we DO want her to do, etc. But she *does* indicate very forcefully (or through limp body) what she does NOT want to do. Including hitting, pinching or trying to bite me. It's hella trying to me as a parent! It's a rough time but I'm generally not of the persuasion of getting her to behave in a predetermined fashion kind of parent. We all want our children to "play nice" and be perfectly behaved ... but it just isn't reality sometimes. Particularly at this age they are beginning to assert their individuality, but this will be a recurring theme, I think, throughout childhood and certainly in adolescence. As much as possible letting go of expectations and "should"s - ie, My son "should" be gentle and "should"n't hit me" will help us to be less stressed out as parents and hopefully will foster a sense of partnership between parent and child.
I try to view things from her perspective, and this generally helps. She has ideas of how and what she wants to do -- this is a good thing! She is growing into herself, into her autonomy. I try to foster this independence as much as I can, since I see this as an important part of my role as a parent. So I reconsider what I have asked for that she is refusing to do - if possible, I revise MY expectations. If it's not possible- if we HAVE TO LEAVE THE HOUSE RIGHT NOW! for example, I try to build choice into her moments: "We are going driving in the car. Do you want to take this ball or this teddy bear in the car with us?" This helps to give her some power over her life in a situation where she is essentially powerless - we're getting in the car and going, eventually if not now. There's also the emotional aspect of things- more about that below.
Also asking questions like, "Do you want to do that yourself? Or do you want Daddy/Mami help you?" (That usually results in her doing it by herself pretty quickly-- Daddy or Mami helping is not nearly as fun! and sometimes downright horrible torture as far as she is concerned)
During the hitting/pinching what I do is to verbalize what she might be feeling (if I can figure out what's going on)- "You are frustrated because I won't let you throw the blocks." Basically and rather loosely I do SALVE from Naomi Aldort's books. S- self talk (this includes recognizing the "shoulds") A- attention, pay attention to my daughter, coming back to her and what's going on with her L- listen to what she is trying to communicate V- validate, validating her emotions instead of negating them E- empower her to find her own solution. The last is the hardest for me, and maybe for all parents of toddlers? because sometimes they don't know what the solution is and you can see a solution. But our solution as a grown up may be very different from the solution that a child comes up with. When I let the tantrum play out often Thalia's solution is nursing- reconnecting with me. Now, this doesn't mean I let her hit/pinch me! I either hold her hands gently but firmly or I put her on the floor next to me but out of reach of my neck (which is what she wants to pinch- of course! how does she KNOW so well that that hurts like hell?!). I keep my voice calm. I do let her know that pinching/hitting hurts but without getting angry (or at least, showing my anger) or hysterical. Toddlers have so many emotions that they are just getting used to having and I think it's often overwhelming for them. So learning as a parent to recognize this is essential.
If you are a book-learning type (I am) the following books are ones that I have found helpful.
Unconditional Parenting - Alfie Kohn
Raising Our Children, Raising Ourselves - Naomi Aldort
The Emotional Life of the Toddler - Alicia Lieberman
How to Talk so Kids will Listen and Listen so Kids will Talk - Adele Faber & Elaine Mazlish
Good luck! Sorry if this seems like a huge long lecture-- don't mean it to! But this is like the one thing I actually think a lot about and practice a lot with Thalia. You are sooooooo not alone as the parent of an almost two year old!!!!

(by the way: key word is "practice" -- am so not perfect at doing all of this, working through this new relationship with Thalia, but it's a journey the two of us, three of us with my husband who is very involved parent, are on, and if I don't expect perfection from myself it's easier to pick up the pieces and try again!)