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We report on measurements on inclusive cross sections times branching fractions into electrons for W and Z bosons produced in $p\overline{p}$ collisions at $\sqrt{s}=1.8\mathrm{TeV}.$ From an integrated luminosity of 84.5 ${\mathrm{pb}}^{\mathrm{\ensuremath{-}}1}$ recorded in 1994--1995 using the D\O{} detector at the Fermilab Tevatron, we determine $\ensuremath{\sigma}(p\overline{p}\ensuremath{\rightarrow}W+X)\ifmmode\times\else\texttimes\fi{}B(\stackrel{\ensuremath{\rightarrow}}{W}e\ensuremath{\nu})=2310\ifmmode\pm\else\textpm\fi{}10(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}50(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}100(\mathrm{lum})\mathrm{pb}$ and $\ensuremath{\sigma}(p\overline{p}\ensuremath{\rightarrow}Z+X)\ifmmode\times\else\texttimes\fi{}B(\stackrel{\ensuremath{\rightarrow}}{Z}ee)=221\ifmmode\pm\else\textpm\fi{}3(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}4(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}10(\mathrm{lum})\mathrm{pb}.$ From these, we derive $\ensuremath{\sigma}(p\overline{p}\ensuremath{\rightarrow}W+X)\ifmmode\times\else\texttimes\fi{}B(\stackrel{\ensuremath{\rightarrow}}{W}e\ensuremath{\nu})/\ensuremath{\sigma}(p\overline{p}\ensuremath{\rightarrow}Z+X)\ifmmode\times\else\texttimes\fi{}B(\stackrel{\ensuremath{\rightarrow}}{Z}ee)=10.43\ifmmode\pm\else\textpm\fi{}0.15(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.20(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}0.10(\mathrm{NLO}),$ $B(\stackrel{\ensuremath{\rightarrow}}{W}e\ensuremath{\nu})=0.1044\ifmmode\pm\else\textpm\fi{}0.0015(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.0020(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}0.0017(\mathrm{theory})\ifmmode\pm\else\textpm\fi{}0.0010(\mathrm{NLO}),$ and ${\ensuremath{\Gamma}}_{W}=2.169\ifmmode\pm\else\textpm\fi{}0.031(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.042(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}0.041(\mathrm{theory})\ifmmode\pm\else\textpm\fi{}0.022(\mathrm{NLO})\mathrm{GeV}.$ We use the latter to set a 95% confidence level upper limit on the partial decay width of the W boson into nonstandard model final states, ${\ensuremath{\Gamma}}_{W}^{\mathrm{inv}},$ of 0.213 GeV. Combining these results with those from the 1992--1993 data gives $\ensuremath{\sigma}(p\overline{p}\ensuremath{\rightarrow}W+X)\ifmmode\times\else\texttimes\fi{}B(\stackrel{\ensuremath{\rightarrow}}{W}e\ensuremath{\nu})/\ensuremath{\sigma}(p\overline{p}\ensuremath{\rightarrow}Z+X)\ifmmode\times\else\texttimes\fi{}B(\stackrel{\ensuremath{\rightarrow}}{Z}ee)=10.51\ifmmode\pm\else\textpm\fi{}0.25,$ ${\ensuremath{\Gamma}}_{W}=2.152\ifmmode\pm\else\textpm\fi{}0.066\mathrm{GeV},$ and a 95% C.L. upper limit on ${\ensuremath{\Gamma}}_{W}^{\mathrm{inv}}$ of 0.191 GeV. Using a sample with a luminosity of 505 ${\mathrm{nb}}^{\mathrm{\ensuremath{-}}1}$ taken at $\sqrt{s}=630\mathrm{GeV},$ we measure $\ensuremath{\sigma}(p\overline{p}\ensuremath{\rightarrow}W+X)\ifmmode\times\else\texttimes\fi{}B(\stackrel{\ensuremath{\rightarrow}}{W}e\ensuremath{\nu})=658\ifmmode\pm\else\textpm\fi{}67\mathrm{pb}.$