Notation: $\varphi$ and $\phi$ Is it bad style to use $\phi$ and $\varphi$ in the same paper (for different things, of course)?
I'd like to use $\phi$ for a function and $\varphi$ for a particular function value.
 A: It is not uncommon to use the same letter from different fonts in the same paper to denote different things. 
For example I could see easily somebody using $A_n$ for some matrix and $\mathfrak{A}_n$ for the alternating group on $n$ symbols. 
Thus, I do not think there is something wrong in principle with using $\phi$ and $\varphi$ in the same paper. For example, you might want to have one phi for use as an angle and one for Euler's totient function. 
However, your specific idea of having one as the function and the other as the value of the function strikes me as not so good, specifically as it will be hard to recall which is which. The idea proposed in a comment to rather use uper and lower case instead seems good.  
A: Yes, it is bad style. Not everyone are used to distinguishing mentally between these variants of lower-case phi, so making a distinction will make the paper harder to read. It would be akin to making a distinction between loop-tailed $g$ and open-tailed $g$ in otherwise the same typeface/style.
It will also make it harder for someone to quote and discuss your formulas and results if they're using a medium where one cannot easily distinguish the variants.
