Polymers such as wax definitely undergo phase transitions. You inquired about paraffin wax, which is oil-based.
Paraffin wax is made of long rod-like molecules called linear straight-chain alkanes. It's solid at room temperature, but when refined as liquid paraffin and combined with water, it can act as liquid crystal, which complicates its phase diagram.
Liquid crystal is a phase all to itself. There are other phases within the liquid crystal phase. In the nematic phase, the long rod-like paraffin molecules all point in the same direction but have no positional structure. In the smectic phase, molecules tend to form layers (for example, slippery soap that collects in the bottom of a soap dish is smectic liquid crystal). In the cholesteric phase, the layers corkscrew around an imaginary axis. Here's a description of these and other liquid crystal phases: http://plc.cwru.edu/tutorial/enhanced/files/lc/phase/phase.htm.
The phase diagrams of polymers like paraffin may not look like the phase diagrams you're familiar with. Depending on how the paraffin molecule is altered in refining, its phase attributes will change. It may be liquid at room temperature, or solid. The phase diagram may change if paraffin combines with water, because when treated with other materials it can be a surfactant/emulsifier. One end of the molecule can be hydrophilic while the other is hydrophobic, and in that case the phase diagram will be altered. Unlike a pure element, paraffin can have many phase diagrams depending on the refinery process that produced it, additives, and other substances with which it combines.
One reason you may have trouble noticing the phase transitions of wax is that heat doesn't flow immediately through a wax blob. The outer layers soften and liquify first. Here's a link to a study of phase transitions in paraffin: http://www.ijettjournal.org/volume-2/issue2/IJETT-V2I2P213.pdf.
Chocolate is not a polymer, but inexpensive chocolate may be mixed with paraffin to give it polymer-like qualities such as surface sheen and smoothness. When you're dealing with composite substances such as chocolate, the phase diagram may not plot pressure against temperature. For example, here is a link to a study of the six polymorphic phases of chocolate: http://link.springer.com/article/10.1007%2Fs11746-998-0245-y. And here is an explanation of those phases: http://patentimages.storage.googleapis.com/WO2012135279A1/imgf000006_0001.png. Here's a phase diagram that plots cooling time against temperature, which shows how chocolate needs the optimal combination of temperature and cooling time to form the most desirable phase structure (scroll down to the phase diagram): http://soft-matter.seas.harvard.edu/index.php/The_Science_of_Chocolate:_interactive_activities_on_phase_transitions,_emulsification,_and_nucleation.