> Are there any Sage functions and/or classes for computing Newton
> Polygons?

Yes there are, here's some quick examples.

sage: R.<x,y> = PolynomialRing(QQ)
sage: p = 1 + x + y + x^2*y
sage: P = p.newton_polytope()
sage: P.vertices()
[[2, 1], [1, 0], [0, 1], [0, 0]]
sage: P.show()
# picture of newton polytope appears in web browser
sage: R.<u,v,w> = PolynomialRing(QQ)
sage: p = (1 + u)*(1 + v)*(1 + w)
sage: P.
Display all 149 possibilities? (y or n)
sage: P = p.newton_polytope()
sage: P.show()
# cube appears in JMol

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