Adjunct faculty can use Interlibrary Loan services if they have the correct affiliation with the university listed in Banner. You can check that affiliation by logging into OneCampus then selecting Manage Accounts, then Profile. You'll need to see VT-ACTIVE-MEMBER or VT-AFFILIATE listed under Affiliations, at the bottom of the page, to be able to login to ILLiad.
If you don't have one of those affiliations, talk with your sponsor or your department's HR representative about what you need to do to gain that affiliation. The library has no ability to change your affiliation with the university.