You may want to use perl regex instead.
perl -pe 's|<strong>(.*?)</strong>|\\textbf{\1}|g'
Your problem is similar with non-greedy-regex-matching-in-sed. And next time you may want to simplify your case to point out the real problem. For example, don't just paste the raw html code, use this instead:
fooTEXT1barfooTEXT2bar
Update
If you just want the greedy approach, just ignore this.