NO. As a Egyptian national even with a valid USA visa or Saudi
residency, you are not eligible to enter Armenia. Answer is from
official Armenia Ministry of foreign
affairs.
Citizens of Egypt are listed who require a visa with invitation only from official ministry of foreign affairs website.
Invitations
You can see the list of countries, citizens of which can obtain
Armenian visa only upon invitation and only at the diplomatic
representations of consular offices of the Republic of Armenia here.
Armenian nationals who are citizens of those countries can obtain
Armenian visa without invitation and upon arrival.
Invitations can be submitted to the Ministry of Foreign Affairs by
a) juridical persons registered in Armenia
b) authorities of Armenia and diplomatic representations or
international organizations or their representatives (physical persons
submit invitation to the Passport and Visa Department of the Police)
what type and sort of invitation require can be found on this link.
http://www.atb.am/en/tourist/visa/
Also Visa and Passport confirms the same answer from their search engine.
National Egypt (EG) /Embarkation Saudi Arabia (SA)
Destination Armenia (AM)
Visa Information
Armenia (AM)
Passport required.
- Passports and other documents accepted for entry must be valid for the period of intended stay. Passport Exemptions:
- Passengers with an emergency or a temporary passport.
Visa required.
Additional Information:
- Visitors are required to hold proof of sufficient funds to cover their stay and documents required for their next destination.