Our BON has a library of position statements that can provide answers. You can find them at Position Statements
IM, SQ and 'injectable' meds are definitely within the scope of LVN practice - this is included in LVN curriculum.
The BON has determined that IV therapy & IV related tasks are not part of LVN curriculum, therefore the employer must provide this training and validate competency before allowing its employed LVNs to perform these tasks. So, it is up to the employer to manage IV therapy/IV meds & hang blood. Since our nurse practice act specifically states that RNs may not delegate patient assessment - - the RN is still responsible for 'assessing the patient's reaction to ___________'; whether this is a medication, blood, or anything else. Therefore, the most common arrangement is for first doses of any scheduled IV medication to be administered by an RN so s/he can assess for any possible adverse reactions. Likewise, when blood is administered, the usual practice is for an RN to monitor the patient's initial reaction.
Re: central lines - there are many different types of central lines. LVNs cannot be trained to insert PICC lines (specific ruling by BON), but managing dressing changes is no problem for any type of central lines (PICC, subclavian, jugular, etc). RNs may
be credentialed (by their employing facility) to remove central lines.
"surgical drains" does not provide sufficient information to make a response because their are so many different iterations... you'll need to be more specific.