APA offers PsycNet, which allows you to search everything in PsycINFO. However, you can only receive full text articles by paying a high cost. You can copy the citation into an email and send it to firstname.lastname@example.org. We can't guarantee that we'll be able to supply everything (new articles can be especially hard), but we'll try our best. Usually the turnaround is pretty fast, within a day or two. In limited cases where the article is critical and we can't find it on ILL, we have a small amount of funds set aside to purchase a copy for you.
EBSCO's collection of over 400 journals is available through the AMBS Library thanks to an Indiana State Library subscription.
300 Social sciences
610 Medicine and health
Type in the library search box: "su: psychology" or "su: psychology religion"
You can find these journals in the Atlas collection. Some of these also have back volumes in the library periodical stacks.