Oldershaw, from Burlington, Ont., was second in the men's C-1, 1,000 metres, 1.721 seconds behind Brazil's Isaquias Queiroz dos Santos. Mexico's Jose Cristobal was third.
In the K1 1,000 metres, van Koeverden was 2.065 seconds behind winner Jorge Garcia of Cuba. Daniel Dal Bo of Argentina was second.
The four-time Olympic medallist from Oakville, Ont., led until the final 300 metres but faded to the finish line.
Canada normally sends a B team in canoe/kayak to the Pan Ams, so this marked the Pan Am debut for both van Koeverden and Oldershaw.
Van Koeverden, 33, won gold and bronze at the 2004 Olympics in Athens, plus silver in both the 2008 and 2012 Olympics.
Oldershaw was a bronze medallist at the 2012 London Games.
Later, Ben Russell and Gabriel Beauchesne-Sevigny won gold in the C-2 1,000-metre race with a time of 3:46.316.
The Canadians beat Brazil by 0.801 seconds and Cuba by 3.616 seconds.
Michelle Russell, sister to Ben, won silver in K-1 500-metre event, her second medal of the Pan Am Games. She won Canada's first gold of the Games in the K-4 500-metre event.
Russell finished 1.725 seconds behind Cuba's Yusmari Mengana.