Exhibit 24

POWER OF ATTORNEY

Know all by these presents, that the undersigned hereby constitutes and appoints
each of Theodore (Ted) Ashburn, M.D., Ph.D. and John McCabe of Oncorus, Inc.,
and Marc Recht, Courtney T. Thorne, Lily Colahan and Jason Minio of Cooley LLP,
with full power of substitution, signing individually, the undersigned's true
and lawful attorneys-in fact and agents to:

(1) execute for and on behalf of the undersigned, in the undersigned's capacity
as an officer, director or beneficial owner of more than 10% of a registered
class of securities of Oncorus, Inc., Forms 3, 4, and 5 (including any
amendments thereto), relating to the securities of Oncorus, Inc., in accordance
with Section 16(a) of the Securities Exchange Act of 1934, as amended (the
"Exchange Act") and the rules thereunder and a Form ID, Uniform Application for
Access Codes to File on EDGAR;

(2) do and perform any and all acts for and on behalf of the undersigned that
may be necessary or desirable to execute such Forms 3, 4, or 5, or Form ID
(including any amendments thereto) and timely file such forms with the United
States Securities and Exchange Commission and any stock exchange or similar
authority; and

(3) take any other action of any nature whatsoever in connection with the
foregoing which, in the opinion of such attorney-in-fact, may be of benefit, in
the best interest of, or legally required by, the undersigned, it being
understood that the documents executed by such attorney-in-fact on behalf of the
undersigned pursuant to this Power of Attorney shall be in such form and shall
contain such terms and conditions as such attorney-in-fact may approve in such
attorney-in-fact's discretion.

The undersigned hereby grants to each such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that such attorney-in-fact, or such
attorney-in-fact's substitute or substitutes, shall lawfully do or cause to be
done by virtue of this power of attorney and the rights and powers herein
granted.  The undersigned acknowledges that the foregoing attorneys-in-fact, in
serving in such capacity at the request of the undersigned, are not assuming,
nor is Oncorus, Inc. assuming, any of the undersigned's responsibilities to
comply with Section 16 of the Exchange Act.

This Power of Attorney shall remain in full force and effect until the earliest
to occur of (a) the undersigned is no longer required to file Forms 3, 4 and 5
with respect to the undersigned's holdings of and transactions in securities
issued by Oncorus, Inc., (b) revocation by the undersigned in a signed writing
delivered to the foregoing attorneys-in-fact or (c) as to any attorney-in-fact
individually, until such attorney-in-fact is no longer employed by Oncorus, Inc.
or Cooley LLP.

The undersigned has caused this Power of Attorney to be executed as of September
11, 2020.

/s/ Briggs Morrison, M.D.
Briggs Morrison, M.D.