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How does the syntax work in bash? This is my pseudocode for C style if else statements. For instance:

If (condition)
    then
    echo "do this stuff"

elseif (condition)
    echo "do this stuff"

elseif (condition)
    echo "do this stuff"

    if(condition)
        then
        echo "this is nested inside"
    else
        echo "this is nested inside"

else
    echo "not nested"

Answers

I guess your question is about the dangling else ambiguity contained in many grammars; in bash there isn't such a thing. Every if has to be delimited by a companion fi marking the end of the if block.

Given this fact (besides other syntactic errors) you'll notice your example isn't a valid bash script. Trying to fix some of the errors, you might get something like this

if condition
    then
    echo "do this stuff"

elif condition
    then
    echo "do this stuff"

elif condition
    then
    echo "do this stuff"
    if condition
        then
        echo "this is nested inside"
    # this else _without_ any ambiguity binds to the if directly above as there was
    # no fi closing the inner block
    else
        echo "this is nested inside"

    #   else
    #       echo "not nested"
    #  as given in your example is syntactically not correct !
    #  We have to close the  last if block first as there's only one else allowed in any block.
   fi
# now we can add your else ..
else
   echo "not nested"
# ... which should be followed by another fi
fi