Oil refiner stocks could rally despite the commodity taking a dive on Monday, CNBC "Fast Money" trader Guy Adami said.

West Texas Intermediate crude fell more than 7 percent Monday, hitting its lowest level since April. Adami liked Tesoro and Valero, which both rose on the day despite the sharp drop in oil.

Trader Dan Nathan, though, would avoid the oil sector as giants such as ExxonMobil slid on Monday.

"I don't think you want to get near this space," he said.

Read MoreOil crushed as correction gains momentum

Some traders also looked to airline stocks, which benefit from cheaper oil prices. United Continental Holdings and Delta Air Lines, which climbed more than 4 and 1 percent on Monday, respectively, have "upside" moving forward, said trader Pete Najarian.

JetBlue—which rose about half a percent on Monday—has "traded really well" with a more than 30 percent gain on the year, Adami said. He said investors should hold on to the stock into JetBlue's quarterly results report, which is slated for later this month.

Disclosures:

Pete Najarian

Long AMAT, AAPL, BAC, BMY, BP, CSX, DISCA, DKS, FOXA, GE, KKR, KO, LLY, MRK, PEP and PFE. He is long calls AAPL, ABX, BAC, BBY, C, CY, DAL, ETFC, FCAU, INVN, JPM, LULU, LVS, NUAN, OC, ORCL, PNR, S, SYY, UAL, USB, VOYA, VZ, WYNN, XLF and ZIOP. Today, he bought C calls.

Dan Nathan

Dan is long JPM July put spread, TJX Aug put, CAT July/August put spread, TWTR, TWTR SEPT call spread, SO, INTC July put, LVS July Aug put spread, MSFT July call fly and WDAY July call fly. He is short SO Aug calls.

Karen Finerman

Karen is long BABA, BAC, C, FINL, FL, GOOG, GOOGL, JPM, KORS, M and URI. She is short SPY. Her firm is long ANTM, AAPL, BAC, C, DIS, FBT, FINL, FL, GOOG, GOOGL, GPS, IBB, JPM, KORS, M, SUNE, URI, XBI, KORS call spreads, URI calls, KORS puts and SPY puts. Her firm is short IWM, SPY and MDY. Karen Finerman is on the board of GrafTech International.

Guy Adami

Guy Adami is long CELG, EXAS and INTC. Guy Adami's wife, Linda Snow, works at Merck.