Polymers which are miscible in oil
Plastics Design Library series include tabulated parameters for the variety of polymers.
One of such parameters is a PDL number rating from 0 to 9:

0: solvent dissolved disintegrated
1: decomposition
2: severe distortion; oxidizer and plasticizer deteriorated
…
9: highest resistance, no change

In the table below I assembled data on thermoplastics chemically unstable towards various oils with PDL numbers below 3:

$$
\begin{array}{lrcll}
\hline
\textbf{Polymer} &amp; \boldsymbol{T/\pu{°C}} &amp; \textbf{PDL} &amp; \textbf{Oil} &amp; \textbf{Resistance Note} \\
\hline
\text{CAB} &amp; 20 &amp; 0 &amp; \text{spearmint oil} &amp; \text{Limited Resistance} \\
\hline
\text{LDPE} &amp; 20 &amp; 1 &amp; \text{aniseed oil} &amp; \text{Not resistant; tensile strength at yield and elongation at break greatly reduced} \\
\hline
\text{HDPE} &amp; 20 &amp; 2 &amp; \text{camphor oil} &amp; \text{Not resistant} \\
\hline
\text{PP} &amp; 100 &amp; 2 &amp; \text{two-stroke engine oils} &amp; \text{Unsatisfactory/severe effect} \\
  &amp; 20 &amp; 2 &amp; \text{turpentine oil} &amp; \text{Not resistant} \\
  &amp; 100 &amp; 2 &amp; \text{vaseline oil} &amp; \text{Unsatisfactory/severe effect} \\
\hline
\text{LLDPE} &amp; 20 &amp; 1 &amp; \text{aniseed oil} &amp; \text{Not resistant; tensile strength at yield and elongation at break greatly reduced} \\
\hline
\text{PS} &amp; 22 &amp; 2 &amp; \text{clove oil} &amp; \text{Not resistant; plastic severely crazed; softened or dissolved} \\
  &amp; 22 &amp; 2 &amp; \text{lemon peel and oil} &amp; \text{Not resistant; plastic severely crazed; softened or dissolved} \\
  &amp; 22 &amp; 2 &amp; \text{orange peel and oil} &amp; \text{Not resistant; plastic severely crazed; softened or dissolved} \\
  &amp; 22 &amp; 2 &amp; \text{pine needle oil} &amp; \text{Not resistant; plastic severely crazed; softened or dissolved} \\
  &amp; 22 &amp; 2 &amp; \text{spearmint oil} &amp; \text{Not resistant; plastic severely crazed; softened or dissolved} \\
\hline
\text{SAN} &amp; 23 &amp; 2 &amp; \text{citronella oil} &amp; \text{Severe attack; softened in few hrs} \\
  &amp; 23 &amp; 2 &amp; \text{clove oil} &amp; \text{Severe attack; softened in few hrs} \\
  &amp; 22 &amp; 2 &amp; \text{lemon peel and oil} &amp; \text{Not resistant; plastic severely crazed; softened or dissolved} \\
  &amp; 52 &amp; 2 &amp; \text{pine needle oil} &amp; \text{Severe attack; softened in few hrs} \\
  &amp; 23 &amp; 2 &amp; \text{spearmint oil} &amp; \text{Severe attack; softened in few hrs} \\
\hline
\text{ABS} &amp; 52 &amp; 2 &amp; \text{pine needle oil} &amp; \text{Severe attack; softened in few hrs}  \\
  &amp; 23 &amp; 2 &amp; \text{spearmint oil} &amp; \text{Severe attack; softened in few hrs} \\
\hline
\end{array}
$$

Acronyms

$$
\begin{array}{ll}
\text{CAB} &amp; \text{Cellulose Acetate Butyrate} \\
\text{LDPE} &amp; \text{Low Density Polyethylene} \\
\text{HDPE} &amp; \text{Polyethylene} \\
\text{PP} &amp; \text{Polypropylene} \\
\text{LLDPE} &amp; \text{Linear Low Density Polyethylene} \\
\text{PS} &amp; \text{Polystyrene} \\
\text{SAN} &amp; \text{Styrene Acrylonitrile Copolymer} \\
\text{ABS} &amp; \text{Acrylonitrile Butadiene Styrene}
\end{array}
$$

References


Chemical Resistance of Thermoplastics; Woishnis, W. A., Ebnesajjad, S., Eds.; Plastics Design Library; William Andrew: Norwich, N.Y, 2012.