As for tutorials on SoapUI, sadly the majority of them are sub-par at best and out of date. If you want to learn SoapUI the best option is likely to jump in feet first and hit the ground running.
My background is primarily API testing, with a specialty with SoapUI and Groovy, so I will try and give some hints and pointers to get you started.
SoapUI's core only transmits data
In it's core, all SoapUI does is open up a socket and sends and receives a request. This is an extremely simple concept that once you understand, it will make your life a lot easier. The ability to change this request on the fly is where SoapUI becomes difficult. This is where the scripting language, groovy, comes into play.
Groovy is Java's little brother
Learning Java will drastically improve your skillset with SoapUI's groovy scripting language. The majority of the skill with SoapUI is in the Groovy scripting, so if you want to become an expert in API testing and SoapUI, learn Java and Groovy.
Learn APIs inside and out
Learn all about APIs. A decent place to start is the SoapUI API Dojo. It covers a brief overview of APIs and the future of them. The second step I would take would be developing a very basic API using Java or C# in order to learn how APIs work and the type of code that is being developed for them. Also, if you use Java, this will strengthen your Groovy skills.
Leverage the SoapUI API
Leveraging the SoapUI API for information and learning how to google it will become extremely beneficial. They use a rather odd but easy to understand naming convention that will make it a little bit easier to navigate.
Learn by using SoapUI Source
As an open source project, you can import SoapUI into Java projects and dig through the source code. By importing into a Java project this will give you a better intellisense style functionality and allow for you to understand the objects within the scripting language a lot easier. Afterwards, you can easily convert the majority of Java projects into Groovy script and use them in SoapUI's groovy directly, build add ons or even run it directly from a Java project.
Become an active member on the SoapUI forums
And last but definitely not least, be active on the SoapUI forums. Both asking and answering questions. My name there is PaulM, feel free to contact me if you ever need anything, but first ask questions and become familiar with the site. This will lead to a lot more experience than most anything else can give you in API testing since you will be helping and reading a variety of different problems and solutions that other people have ran into with SoapUI.
And some references that will help you get started
SoapUI's Rest Guide
LearnSoapUI Blog <-- Very useful for scripting help
Ole Lensmar's (CTO of Smartbear) Blog <---- Very useful for Plugin development
Example Groovy Scripts