Because we have no bib entrys you use I simply used the example bib file biblatex-examples.bib. The bib entrys kastenholz,sigfridsson,ctan,markey have dois and urls included to test the code.
To get a better layout add the three following lines to your code:
\setcounter{biburlnumpenalty}{8000} % <=================================
\setcounter{biburlucpenalty}{8000} % <=================================
\setcounter{biburllcpenalty}{8000} % <=================================
You can change the number 8000 as you need (1 to 10000).
With the following MWE I have no problems with the margins and dois or urls:
\RequirePackage{filecontents}
\begin{filecontents}{\jobname.bib}
@Article{Hsi_JACS_1975,
author = {Edward Hsi and Robert G. Bryant},
title = {Nuclear magnetic resonance relaxation in frozen lysozyme solutions},
journal = {J. Am. Chem. Soc.},
year = {1975},
volume = {97},
number = {11},
pages = {3220--3221},
doi = {10.1021/ja00844a051},
eprint = {dx.doi.org/10.1021/ja00844a051},
url = {dx.doi.org/10.1021/ja00844a051},
}
@Article{Brovchenko_ChemPhysChem_2008,
author = {Ivan Brovchenko and Alla Oleinikova},
title = {Multiple Phases of Liquid Water},
journal = {Chem\-PhysChem},
year = {2008},
volume = {9},
number = {18},
pages = {2660--2675},
issn = {1439-7641},
doi = {10.1002/cphc.200800639},
keywords = {percolation, phase diagrams, phase transitions,
supercritical fluids, thermodynamics},
publisher = {WILEY-VCH Verlag},
url = {dx.doi.org/10.1002/cphc.200800639},
}
\end{filecontents}
\documentclass{article}
\usepackage[%
backend=bibtex,
style=phys,
biblabel=brackets,
natbib=true,
sorting=none,
url=true,
hyperref=auto
]{biblatex}
\usepackage[autostyle=true]{csquotes}
\addbibresource{biblatex-examples.bib}
\addbibresource{\jobname.bib}
\setcounter{biburlnumpenalty}{8000} % <=================================
\setcounter{biburlucpenalty}{8000} % <=================================
\setcounter{biburllcpenalty}{8000} % <=================================
\begin{document}
Test \cite{kastenholz,sigfridsson,ctan,markey}
test \cite{Hsi_JACS_1975,Brovchenko_ChemPhysChem_2008} test
\printbibliography[heading=bibintoc]
\end{document}
with the resulting page:

Please try this MWE with your own bib entrys. If you still have problems please add theese bib entrys to your question. Then we can test them on our computers ...
biblatex? – Bernard Jul 23 '17 at 14:38\setcounter{biburlnumpenalty}{8000}. – Bernard Jul 23 '17 at 14:45biburlucpenaltyandbiburllcpenalty, see also URL line breaks with biblatex. If you want us to investigate your special problem, please show us the code for some of the problematic.bibentries as well. And make sure that the problematic URLs actually have the problem in the MWE. That way we can be sure to talk about the same thing. – moewe Jul 24 '17 at 11:05