First time spriting a walrus, help appreciated.

[megaMasquerain]

I don't think -jagged- outlines are really the problem outline-wise... more like really straight outlines. Straight, diagonal 1px outlines.

Anyways. In addition to that (and the anatomy concerns which I'm not going to address cause I suck at it too) - contrast, hueshifting/palette size reduction and banding are things you could try and work on.

There should be definitions of contrast and banding in the TSR dictionary, but a quick overview:

Banding = lines of pixels that "hug" each other almost exactly. See - the shadow on the soldier's neck
Contrast = The shade and hue difference between colors. You want your shades to pop most of the time, especially on shiny surfaces like metal! Try making light browns more orange/yellow, dark blues more purple...
Palette size reduction = I don't know if there's a proper term for this one, but try and use as few colors as you can. If you can re-use a color somewhere without it looking awkward, do it! And try it even if you think it would look REALLY weird. For example, on the creature in my signature/avatar, I reused the dark grey for the metal as the darkest shade of the fur on the body. To get used to this, I would recommend challenging yourself by making pieces with only 5-6 colors (or less, if you can manage).

Anyways, I meant to post this earlier but I got REALLY carried away doing an edit of the first sprite in your post. I'm not the best artist out there (far from it) but see if you can spot some techniques I used in comparison to your own