Okay, first problem. You're using at least three different separate pixel sizes on the same sprite. Never do this. It looks extremely inconsistent, like you're just mixing several objects that were never meant to go together. Stick to a single pixel size. Pick a single sprite resolution, and
use it. Want it to be pixellated? Use a low resolution and stick to it. Don't just randomly make huge squares out of several pixels. Want it to be smoother? Then make
all the parts of that sprite that smooth. Don't mix both styles in the same sprite. It'll always look off.
Instead of mixing resolutions, try something closer to this:
Secondly. Colors. You're using something like 11 colors, but because of the way you're using them (contrast to placement) you might as well be using 5. It doesn't look clean. Handle your colors well and use some better contrast between shades. You don't need that many colors if you're going for such a simplisting monochromatic look. Decrease your color count and I guarantee it'll look at least somewhat better:
You're also using the colors in some pretty weird ways, especially in the cape of the idle sprite, where you have some random lines with little to no purpose. Then in the running sprite you're actually managing to create the illusion of a flowing cape. Try to do more of that. Also, I understand the character is supposed to have white and gray colors, but you still should
always use some coloring within your sprites or it'll just look dull. In real life, nothing is 100% white, or 100% gray. Everything has a color, if only slightly. Also shadows tend to have a different color than lights. No object will ever be completely gray in light and completely gray in shadow. There's more than one way to do this right, and several ways to do it
better than this example, but here's a bit of an idea on how to improve coloring:
Finally, stick to a lightsource. The way the cape is shaded implies that the light is coming from the right. The hood, however is lit from... Somewhere? Think about the direction you want the light to come from, and light all elements consistently. It may be a low-res 2D image, but if you want to shade it, you should still absolutely think of each shape as a 3D object, and how it interacts with light. Again, there's a nearly infinite amount of ways to do this right, but here's just a single possible example:
Worth repeating once again: There's no single correct way to do this, you might find your own way to make things work for you, just try experimenting! But even if there's no single way to do it
right there's always a way to do it
better. And I hope these tips help you find the way to do just that. Whatever you do, the single most important thing is consistency. Stick to a single resolution. Stick to a single palette. Stick to a single lightsource (Or even a lack of one!). Stick to a single style. But you can pretty much go crazy otherwise.