C

$A$、$\because \frac{a}{b}=\frac{1}{2}$，$\frac{c}{d}=\frac{4}{8}=\frac{1}{2}$，$\therefore \frac{a}{b}=\frac{c}{d}$，故四条线段$a$，$b$，$c$，$d$是成比例线段，不符合题意；
$B$、$\because \frac{a}{b}=\frac{1}{\sqrt{3}}$，$\frac{c}{d}=\frac{\sqrt{5}}{\sqrt{15}}=\frac{1}{\sqrt{3}}$，$\therefore \frac{a}{b}=\frac{c}{d}$，故四条线段$a$，$b$，$c$，$d$是成比例线段，不符合题意；
$C$、$\because \frac{a}{b}=\frac{2}{4}=\frac{1}{2}$，$\frac{c}{d}=\frac{5}{15}=\frac{1}{3}$，$\therefore \frac{a}{b}≠\frac{c}{d}$，故四条线段$a$，$b$，$c$，$d$不是成比例线段，符合题意；
$D$、$\because \frac{a}{b}=\frac{\sqrt{2}}{2}$，$\frac{c}{d}=\frac{\sqrt{7}}{\sqrt{14}}=\frac{\sqrt{2}}{2}$，$\therefore \frac{a}{b}=\frac{c}{d}$，故四条线段$a$，$b$，$c$，$d$是成比例线段，不符合题意.
故选：$C$.