My Anet A8 prints have been looking squished
It could be that cheap filament has inconsistent diameter, or your calibration is over extruding, or you have something loose that needs to be tight.  It's hard for me to tell precisely from just these images.  In your shoes, I would print 20mm x 20mm x 10mm, 100% infill boxes until I got it dialed in so that it is square, fully filled in, but nice and flat.

If they're coming out square and staying stuck to the build plate properly, but are bumpy and overfilled, then you're over extruding and you'll want to either recalibrate e-steps or if they're correct, adjust your flow rate in the slicer (down).

If they aren't square then you need to square up your frame and tighten it and the belts.

Etc.

But my first guess is that you're extruding too much plastic since I'll bet they were flatter when they were still on the build plate, yes?

On the question of ooze: you'll always get some ooze.  Molten plastic and gravity means some will ooze out pretty much no matter what.  What you need to worry about is when this results in stringing or unwanted lines on the surface of the print.  These things you address with retraction (which reduces the pressure on the nozzle during travel moves, but can't stop gravity) and for the surface problem various travel, z-hop and combing strategies depending on your slicer.