可以通过使用Java的动态编译器和反射机制来实现在Android apk中下载并运行可执行的Java模块。具体步骤如下：

1. 构建Java源文件，例如MyRunnable.java：

public class MyRunnable implements Runnable {
    @Override
    public void run() {
        System.out.println("Hello from MyRunnable!");
    }
}

2. 使用Java Compiler API将Java源文件编译成字节码文件：

JavaCompiler compiler = ToolProvider.getSystemJavaCompiler();
int result = compiler.run(null, null, null, "MyRunnable.java");
if (result != 0) {
    System.out.println("Compilation failed!");
}

3. 将字节码文件保存到dex文件，例如MyRunnable.dex：

DexClassLoader classLoader = new DexClassLoader("MyRunnable.dex", getDir("dex", 0).getAbsolutePath(), null, getClassLoader());

4. 通过反射机制实例化并运行可执行的Java模块：

Class myRunnableClass = classLoader.loadClass("MyRunnable");
Runnable myRunnable = (Runnable) myRunnableClass.newInstance();
myRunnable.run();

完整代码示例如下：

import javax.tools.JavaCompiler;
import javax.tools.ToolProvider;
import dalvik.system.DexClassLoader;

public class MainActivity extends Activity {
    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        String javaCode = "public class MyRunnable implements Runnable {\n" +
                "    @Override\n" +
                "    public void run() {\n" +
                "        System.out.println(\"Hello from MyRunnable!\");\n" +
                "    }\n" +
                "}";

        JavaCompiler compiler = ToolProvider.getSystemJavaCompiler();
        int result = compiler.run(null, null, null, javaCode);
        if (result != 0) {
            System.out.println("Compilation failed!");
            return;
        }

        DexClassLoader classLoader = new DexClassLoader("MyClass.dex", getDir("dex", 0).getAbsolutePath(), null, getClassLoader());

        try