The United Nations Law Collection (UNLC), located in HeinOnline at http://heinonline.org.proxy.uchicago.edu/HOL/Index?collection=unl&set_as_cursor=clear, includes PDFs of multilateral and bilateral treaties published in the United Nations Treaty Series (U.N.T.S.). You can retrieve UN treaty PDFs by using the Get Citation feature.
Besides being able to get U.N.T.S. (and L.N.T.S.) treaties by citation, you can also search for treaties by Title, Popular Name, Country/Party, Text, Signature Date, Signature Place, Treaty Description, and "Kavass Subjects". With this last feature, you can search for all treaties on "piracy", for instance. Note that not all treaties are tagged with "Kavass Subjects", so use a combination of searches to be thorough. The UNLC has a separate list of "International Agreements By Popular Name" and links to "Scholarly Writings" of over 50 faculty members. The UNLC includes an external link to the free United Nations Audiovisual Library of International Law (AVL) - another source for UN law publications in PDF.
There is a "Treaties and Agreements Library" in HeinOnline. This includes sources of treaties and other international agreements to which the U.S. is a party. It does not include the U.N.T.S. The U.N.T.S. is an alternate source of treaties to which the U.S. is a party. It also includes non-U.S. treaties. To access the U.N.T.S., you need to use the separate United Nations Law Collection in HeinOnline.
The United Nations Law Collection also includes PDF versions of Multilateral Treaties deposited with the Secretary-General (for status of treaties, texts of declarations and reservations), the League of Nations Treaty Series (L.N.T.S.); ICJ Reports of Judgments, Advisory Opinions and Orders; Reports of International Arbitral Awards (R.I.A.A.); ICJ, International Law Commission (ILC), and UNCITRAL yearbooks; Documents of the United Nations Conference on International Organization (San Francisco, 1945); reports of proceedings of UN conferences; the Treaty Handbook; and other UN law publications.
Forthcoming updates to the United Nations Law Collection will contain ICJ Pleadings and Oral Arguments, the ICJ Bibliography, and Judgements of the United Nations Administrative Tribunal (UNAT). Stay tuned!