Conclusion:
SOAP, REST, ODATA and HTTP protocols are the most important current Web service APIs..
HTTP - HTTP is the native transport layer protocol that can carry plain, soap, json or ODATA messages. For simplicity, we can assume it to be the Father of transport protocols with Children like SOAP, REST and ODATA
SOAP API - It is built upon the XML specification & works with the HTTP protocol. That is why it is perfect for usage across the web applications. However, lately companies have started looking at REST/Odata services due to its light wait, extensibility, navigational properties at resource level. SOAP has been there for a while and can be assumed as the eldest son of HTTP family.
SOAP is more suitable for Enterprise Apps requiring high Security, distributed environments like Payments and financial applications.
REST API - While REST APIs were designed to take advantage of existing protocols & used over any protocol, when used for web APIs it typically takes advantage of HTTP. This means that developers have no need to install additional software when creating a REST API. REST is an architectural pattern that ODATA uses as well. Similarly, REST is a step between SOAP and ODATA and can be assumed as the middle child of the HTTP family.
REST is more suitable for Apps requiring moderate security but high scalability for example Social sites like Twitter, Facebook, Instagram etc.
OData - It has been adopted by a lot of companies including SAP, IBM, Salesforce, Tableau, Databoom, Progress, Red Hat and Dell. This is the newest member of the family for data exchange built on architectural pattern of REST. ODATA can be assumed as the youngest child of the HTTP family with newest and greatest capabilities but lacks in wide adoption. Recently, a lot of new APIs are being developed as ODATA only APIs to prepare for the future challenges of scalability and performance.