Both projects have a licensing statement for the image (on each page you link above, scroll down to "License") and both are a bit of a cop-out. They are clear that Apache Tomcat is licensed under Apache v2 (surprise!) and that OpenJDK is licensed under GPLv2 (with the added classpath exception). They also note that:
As with all Docker images, these likely also contain other software which may be under other licenses
which is a great example of buck-passing and one of many reasons why containers are not a good format for distributing software. But coming back to your question, the licences on the two key parts (tomcat and the openjdk) permit commercial use. Because of the classpath exception in the OpenJDK's licence, you may (for example) choose to treat the combined whole under the Apache licence, which is pretty business-friendly and imposes few obligations on you besides a patent grant.
If it turns out there's other weirdly-licensed rubbish buried in either docker image, that's your problem, but it's probably only an issue if you choose to redistribute, rather than use, and although your question isn't clear, I don't get the impression you intend to do that. Personally, I'd advise you to get an actual sysadmin, and install docker and dependencies directly on a maintainable platform of your choice. But that's not an issue for this site; from a licensing standpoint, I don't see any reason you can't build your company's web offering on top of Tomcat.
Oracle Linux is a completely separate thing, a distribution maintained by Oracle, and has no bearing on your question. And as ever, IANAL/IANYL.