If you can use LuaLaTeX or XeLaTeX, you can load Computer Modern Unicode Serif. This font has polytonic Greek letters based on Computer Modern and the old cbgreek fonts. In order to get the appropriate shapes for Greek text, instead of math symbols, you select the Script=Greek OpenType feature. The \babelfont command handles this automatically.
\documentclass{article}
\usepackage[paperwidth=11cm]{geometry}
\usepackage[english]{babel}
\usepackage{fontspec}
\usepackage{microtype}
\babelprovide[import]{greek}
\newcommand\textgreek[1]{\foreignlanguage{greek}{#1}}
\newenvironment{greek}%
{\begin{otherlanguage}{greek}}%
{\end{otherlanguage}}
\defaultfontfeatures{Scale = MatchLowercase}
\babelfont{rm}
[Scale=1.0, Ligatures={Common, TeX}, Language=Default]{Latin Modern Roman}
\babelfont[greek]{rm}
[Language=Default]{CMU Serif}
\babelfont{sf}
[Ligatures={Common, TeX}, Language=Default]{Latin Modern Sans}
\babelfont[greek]{sf}
[Language=Default]{CMU Sans Serif}
\babelfont{tt}
[Language=Default]{Latin Modern Mono}
\babelfont[greek]{tt}
[Language=Default]{CMU Typewriter Text}
\begin{document}
\begin{greek}
ἄνδρα μοι ἔννεπε, μοῦσα, πολύτροπον, ὃς μάλα πολλὰ
πλάγχθη, ἐπεὶ Τροίης ἱερὸν πτολίεθρον ἔπερσεν:
\end{greek}
\end{document}

I added more \babelfont cases and options than strictly necessary, in order to suppress some warning messages.
If you actually want letters shaped like \theta and \lambda, just load CMU Serif with Script=Default rather than Script=Greek. By default, lowercase Greek math symbols are slanted and uppercase ones are upright, so you could also throw in a \slshape if you want. You could also use \varphi and \vartheta in math mode to make that more consistent with Greek text.
And a version compatible with PDFLaTeX if you need one. Note that the UTF-8 input encoding has been the default since April 2018. PDFLaTeX will therefore understand Greek, if you load the LGR font encoding.
\documentclass{article}
\usepackage[LGR, T1]{fontenc}
\usepackage[utf8]{inputenc} % The default since 2018
\usepackage[paperwidth=11cm]{geometry}
\usepackage[polutonikogreek, main=english]{babel}
\usepackage{microtype}
\DeclareRobustCommand\textgreek[1]{\foreignlanguage{polutonikogreek}{#1}}
\newenvironment{greek}%
{\begin{otherlanguage}{polutonikogreek}}%
{\end{otherlanguage}}
\begin{document}
\begin{greek}
ἄνδρα μοι ἔννεπε, μοῦσα, πολύτροπον, ὃς μάλα πολλὰ
πλάγχθη, ἐπεὶ Τροίης ἱερὸν πτολίεθρον ἔπερσεν:
\end{greek}
\end{document}

XeLaTeXis alsoLaTeX. I guess you mean you use thepdftexengine. – campa Oct 14 '19 at 09:37