Question: I have some questions regarding aforementioned subject:

* Is there a EC equivalent of RSA-OAEP key transport/encryption algorithm ?
* Is ECIES-KEM sufficient ?

Answer: 
Short answer, 
 - yes
 - yes
To be honest I don't really know how to give a longer answer. 
He are some pointers
<http://www.secg.org/download/aid-780/sec1-v2.pdf>
<http://digital.csic.es/bitstream/10261/32674/1/Gayoso_A%20Comparison%20of%20the%20Standardized%20Versions%20of%20ECIES.pdf>
The question is what you mean by "eqivalence". 

RSA-OAEP yields to an RSA encryption scheme providing security against adaptive chosen message attacks (IND-CCA2) in the random oracle model, while plain RSA does not even provide IND-CPA security.

If you mean security (which I assume), then **yes**, ECIES also achieves the same formal security guarantees as RSA-OAEP in the elliptic curve setting. 

If you want an encryption scheme for elliptic curves providing IND-CCA2 security without random oracles, i.e., relying only on standard assumptions, then you can take the elliptic curve version of Cramer-Shoup encryption.

Latter however, is less efficient then ECIES.

If you only require IND-CPA security, you can also use elliptic curve versions of ElGamal encryption.

Finally, while ECIES is a hybrid encryption scheme by design, the others aren't. However, you can turn them into hybrid schemes.