When the Sahara (opened in 1952) closes on May 16, the oldest casino will still be the same as it’s been for many years: the Flamingo, which opened in 1946. The Sahara was the second oldest during those same years.
Now, the second will be the Riviera, which opened in 1955.
Third oldest will be the Tropicana, which debuted in 1957.
The Aladdin opened on New Year’s Day 1966. Of course, the original hotel-casino was imploded, rebuilt from scratch, and sold to Planet Hollywood, so it might not count.
If not, then Caesars Palace would be the fourth oldest, having opened in 1966, a few months after the Aladdin.
Fifth will be Circus Circus, which debuted in 1968.
Your question specified the Strip, but if you account for the rest of Las Vegas, you’d include the Las Vegas Club (it originally opened in 1931, then moved to its present location in 1949), the El Cortez (1941), the Golden Nugget (the casino opened in 1946; the first rooms were added in 1977), Binion’s (1951), the Golden Gate (1955), the Fremont (1956), and the Four Queens (1965).