Why are these Vias of Different Shapes
The top eight pads are octagons, the top four just happen to be very close together. None of the pads are vias, per se, they are landing pads for through-hole parts. The top four for one, probably a connector for AC input, the middle four for another, a solid state relay, the bottom two are likely for soldering wires to directly. You can see the component outlines for part placement.

The octagons are fairly normal for Eagle layout, I believe they're actually the default shape. The long pads are commonly used for soldering wire to, probably because the wire will often stick through the hole then be bent over parallel to the board. The long pad (and in this case additional SMT pad) of exposed copper allows for more solder to be applied between wire and copper to act as a strain relief.