For creating an RSA key pair you need an undefined number of random bytes from the source. The reason for this is that finding primes is indeterministic and hence it may be required that multiple random large numbers are required. In the end this also depends on the details of the key pair generator used.
However, it is possible to use a well seeded DRBG / PRNG for the key pair generation process. A PRNG is a deterministic or pseudo random number generator; it depends on the entropy of the seeds to generate a computationally random stream of bytes. That is: only the seed is truly random, but to an attacker the output of the PRNG is indistinguishable from random.
If a secure PRNG is used then using 256 bits of seed is all you need; for constrained systems you could even bring this down to 128 bits (at the cost of a lower security margin, of course). So if your system has issues generating large amounts of randomness you could seed your own PRNG and inject it into the RSA key pair generator - if that's possible for your runtime.
OAEP is a padding scheme independent on the key pair generation. That is: the calculations performed for key pair generation do not rely on the calculations performed by OAEP. OAEP may be performed on any secure RSA key pair, as many times as required. As per specification it uses
hLen random bytes per usage, which means 32 bytes when SHA-256 is used and 64 bytes for SHA-512.