Did multituberculate mammals have external ears like placentals or marsupials? I know that monotremes do not have them and multies are more closely related to them, so it is possible that they didn't have external ears.

This is a tricky question to answer!

External ears (pinna) don't really leave a mark on the skeleton unless they are large and directional - in which case the external auditory meatus will usually show quite a strong directionality and there may be areas for muscle attachment visible. Multituberculate fossils so far haven't shown either of these indicators - so they almost certainly didn't have rabbit-like ears.

In terms of the inner ear the cochlea seems to have been short and straight in most multituberculates (although some had longer and slightly curved cochlea). This suggests a hearing system less capable of detecting high frequency air-bourne sounds than we find in marsupials and placental mammals - similar to monotremes as you pointed out. But then again, Platypodes and Echidnae have quite unusual and specialist modes of life - most other mainly aquatic mammals have very small or absent external ears (look at water shrews and seals) and other ant-eating species with good defenses also have reduced or absent pinna (see pangolins and giant anteaters).

Some species of multituberculate appear to have been better adapted than others for detecting higher frequency airbourne sound and these probably would have benefitted from some kind of basic external pinna. After all, the multituberculates were a diverse group, so it seems reasonable to assume that they would have displayed a fair amount of variability in their auditory apparatus.

That's a long way of saying that I don't really know, but it seems reasonable to assume that if they did have pinna they probably weren't big or strongly directional - at least for the species that have been found so far.

The latest research usually placed multituberculates as closer to marsupials and placental mammals than monotremes, somewhere along the line of animals leading to the split between marsupial and placental groups. Seeing as both of these do have external ears, and monotremes don't, it seems reasonable to assume that these appeared somewhere along the line leading to marsupials plus placentals, after these split from monotremes. What we can't yet tell however is if this was before or after the multituberculates first appeared, but it narrows it down to a 'possibly' rather than a definite no!