Sekera's deal is worth US$33 million over six years, while Letestu will reportedly earn $5.4 million over three years.
"We've put together something that we think shows progression with pieces we like. We feel good today," Oilers generak manager Peter Chiarelli said.
Sekera had three goals and 20 assists over 73 games with Carolina and Los Angeles last season.
The native of Bojnice, Slovakia, has 31 goals and 128 assists in 486 games with Buffalo, Carolina and Los Angeles.
Letestu had seven goals and six assists in 54 games with the Blue Jackets last season.
The native of Elk Point, Alta., has 58 goals and 69 assists in 318 games with Pittsburgh and Columbus.