Você pode usar sed
para manipulação de string:
echo '$var = <string> 1.11 </string>' | sed -r 's/<string>(.*)<\/string>//g'
retorna
$var = 1.11
Explicação da construção sed
:
sed -r # call sed with regex-option (-r)
's/ # begin of regex (s means "replace, / is the seperator)
<string>(.*)<\/string> # construct that should be replaced (the / has to be escaped with \ here)
/ # seperator
# replacement string ( means "whatever is matched between the () before")
/g' # apply replacement globally (in case it occurs multiple times in the string)