Some variations provide a polyoxalamide polymer comprising: one or more first segments containing at least one repeat unit that includes (i) a branched, aliphatic hydrocarbon species and (ii) first amide groups at internal ends of the repeat unit, wherein the first amide groups are part of oxalamide groups; one or more polymer end groups containing second amide groups that are each covalently bonded directly to one of the first amide groups, wherein the second amide groups are also part of the oxalamide groups, and wherein the oxalamide groups contain —N—C(═O)—C(═O)—N— sequences; and a reacted form of one or more multifunctional amine chain extenders or crosslinkers with an amine functionality of 3 or greater. The polyoxalamide polymer may be present in a lens, a window, a coating, or a film, for example. The polyoxalamide polymer may have UV transparency, visual transparency, NIR transparency, MWIR transparency, and/or LWIR transparency.