Your main problem here is in the understanding of \newtheorem. Since you're using amsthm, let's look at the documentation (specifically, section 3 Theorem numbering):
In addition to the two mandatory arguments, \newtheorem has two mutually
exclusive optional arguments. These govern the sequencing and hierarchy of
the numbering. The numbering mechanism can be thought of this way:
\newtheorem{<env name>}{<text>}[<parent counter>]
\newtheorem{<env name>}[<shared counter>]{<text>}
The <parent counter> is comparable to \numberwithin; that is, numbering will
restart whenever that sectional level is encountered. If a <shared counter> is
specified, numbering will progress sequentially for all theorem elements using
this counter.
You should be using the second version if you want a numbering scheme that shares the same counter. But you've been using the first, which creates a unique counter for every theorem style.

\documentclass{report}
\usepackage{amsthm}
\theoremstyle{definition}
\newtheorem{myde}{Conjecture}[section]% Conjecture is numbered within \section
\newtheorem{mydef}[myde]{Example}% Example uses myde's counter
\newtheorem{mydeg}[myde]{Definition}% Definition uses myde's counter
\newtheorem{my}[myde]{Theorem}% Theorem uses myde's counter
\newtheorem{myd}[myde]{Approach}% Approach uses myde's counter
\newtheorem{lemma}{Lemma}% Lemma uses myde's counter
\newtheorem{corollary}[myde]{Corollary}% Corollary uses myde's counter
\begin{document}
\chapter{Test chapter}
\section{Test section}
\begin{myde}
this is correct
\end{myde}
\begin{mydef}
this one should be Example 1.1.2
\end{mydef}
\begin{myde}
this one should be Conjecture 1.1.3
\end{myde}
\begin{mydeg}
this one should be Definition 1.1.4
\end{mydeg}
\begin{myde}
this one should be Conjecture 1.1.5
\end{myde}
\begin{my}
this one should be Theorem 1.1.6
\end{my}
\end{document}