Well, finally I've got a solution. First of all I'd like to thank StaxMan for a help.
My environment is: Weblogic 11g, CXF 2.7.5
The problem is WLS already contains implementations for StAX API and xml parsers that is why an application doesn't see the Woodstox parser when using CXF.
Here is the pom.xml:
<!-- CXF -->
<dependency>
<groupId>org.apache.cxf</groupId>
<artifactId>cxf-api</artifactId>
</dependency>
<dependency>
<groupId>org.apache.cxf</groupId>
<artifactId>cxf-rt-frontend-jaxws</artifactId>
</dependency>
<dependency>
<groupId>org.apache.cxf</groupId>
<artifactId>cxf-rt-transports-http</artifactId>
</dependency>
and the main part -- the weblogic-application.xml located in the resources/META-INF/ :
<prefer-application-packages>
<package-name>com.ctc.wstx.*</package-name>
<package-name>org.apache.*</package-name>
</prefer-application-packages>
Be aware of the fact that if do so there may occure the "NoClassDefinition" errors. If so, please, add maven dependencies that contain missing classes.
Hope this helps somebody.