Portuguese former Benfica B man Santos, 21, joins on a two-year deal, having previously had youth spells with SC Lourel, Belenenses and Estoril.
Switzerland-born Shalaj, 26, has signed a one-year deal after leaving Romanian side Dinamo Bucharest.
Both players could make their debuts when Vale travel to Bury on Saturday.
Vale's two latest additions take new boss Bruno Ribeiro's total of summer signings for the League One club to 17.
Find all the latest football transfers on our dedicated page.
Port Vale have signed goalkeeper Miguel Santos and winger Gezim Shalaj, who have both been training with the club, subject to international clearance.