Normally evictions are not the reason of a project starting failure. But if you want to get rid of them, which is always good, for every project, follow this:
The first step to clear the project directory.
The next step is to move evicted and old jars to an archive folder outside the Mendix directory. Always move the lowest version ( for example commons-io-2.3.jar , search for the word 'by’ in the list above). The archive folder is used to recover these files. If the project works fine for some time, erase the folder.
Still you might be combining appstore modules with conflicting jars. Try to update all modules to the latest one applicable for your Mendix version.
If that fails move all the jars to another folder, clear the project directory and place them back one by one and start the project. If the project don't start take the next file.
Take care of your own developed jars, in case you have them.
In case you accidently delete jars without the possibility to recover, create a branch line in the modeler of that version and download that version in a separate directory.
Strange is that bcprov-jdk15on-164.jar is preferred over version 1.69. I would remove version 164.