I can reproduce the problem. What I've tested so far:
The HTML we pass to JODConverter contains the bold and italic formatting.
Opening the plain HTML file with LibreOffice shows the bold and italic formatting.
Running libreoffice --headless --convert-to odt export.html breaks the bold and italic formatting.
I've reproduced this also with a minimal example. When strong and em are nested, we're always losing the outer one, the inner one is kept by LibreOffice.
