Using libgdx, how can I add both text and images to a ScrollPane?

If you want to stay with the List you could inherit the list an override the drawItem method, like this:

public class ItemList extends List<Entry<String, String>> {

    private int alignment;

    public ItemList(Skin skin, String styleName) {
        super(skin, styleName);
    }

    @Override
    protected GlyphLayout drawItem (Batch batch, BitmapFont font, int index, Entry<String, String> item, float x, float y, float width) {
        String string = toString(item);

        TextureAtlas.AtlasRegion image = // get the image, you want to draw

        batch.draw(image, x, y-image.regionHeight)

        return font.draw(batch, string, x +image.regionWidth +5, y, 0, string.length(), width -image.regionWidth -5, this.alignment, false, "...");
    }

    @Override
    public void setAlignment (int alignment) {
        this.alignment = alignment;
    }

}

With this method you do not have to reimplement the selection mechanism of the list.

You can't use a list widget to add images or tables or anything other than text as far as I am aware. You can, however, make a table and change the background Drawable to a new Texture which can simulate the effect of a list when some events occur (like a mouseMove event). You can then add that table into a ScrollPane which can handle your scroll events.

This will take you a bit of coding, but here is a working example I whipped up for you:

package <some package>;

import com.badlogic.gdx.Game;
import com.badlogic.gdx.Gdx;
import com.badlogic.gdx.Screen;
import com.badlogic.gdx.graphics.GL20;
import com.badlogic.gdx.graphics.Texture;
import com.badlogic.gdx.graphics.g2d.TextureRegion;
import com.badlogic.gdx.scenes.scene2d.Event;
import com.badlogic.gdx.scenes.scene2d.Stage;
import com.badlogic.gdx.scenes.scene2d.ui.Image;
import com.badlogic.gdx.scenes.scene2d.ui.Label;
import com.badlogic.gdx.scenes.scene2d.ui.ScrollPane;
import com.badlogic.gdx.scenes.scene2d.ui.Skin;
import com.badlogic.gdx.scenes.scene2d.ui.Table;
import com.badlogic.gdx.scenes.scene2d.utils.FocusListener;
import com.badlogic.gdx.scenes.scene2d.utils.TextureRegionDrawable;

public class ScrollScreenTest implements Screen{
    Game game;
    ScrollPane scrollpane;
    Skin skin;
    Stage stage;
    Table container, table1, table2, table3;
    Texture texture1, texture2, texture3;

    public ScrollScreenTest(Game game){
        this.game = game;
    }
    @Override
    public void render(float delta) {
        Gdx.gl.glClearColor(0, 0, 0, 1);    //sets up the clear color (background color) of the screen.
        Gdx.gl.glClear(GL20.GL_COLOR_BUFFER_BIT);  //instructs openGL to actually clear the screen to the newly set clear color.
        stage.draw();
        stage.act(delta);

    }

    @Override
    public void resize(int width, int height) {
    }

    @Override
    public void show() {

        // setup skin
        skin = new Skin(Gdx.files.internal("data/uiskin.json"));

        texture1 = new Texture(Gdx.files.internal("iron_axe.png"));
        texture2 = new Texture(Gdx.files.internal("iron_dagger.png"));
        texture3 = new Texture(Gdx.files.internal("iron_sword.png"));

        // table that holds the scroll pane
        container = new Table();
        container.setWidth(320f);
        container.setHeight(300f);

        // tables that hold the data you want to display
        table1 = new Table(skin);
        table1.add(new Image(texture1)).expandY().fillY();
        table1.add(new Label("", skin)).width(10f).expandY().fillY();// a spacer
        table1.add(new Label("Look at this axe I stole!", skin)).expandY().fillY();

        table2 = new Table(skin);
        table2.add(new Image(texture2)).expandY().fillY();
        table2.add(new Label("", skin)).width(10f).expandY().fillY();// a spacer
        table2.add(new Label("So dagger, much pointy.", skin)).expandY().fillY();

        table3 = new Table(skin);
        table3.add(new Image(texture3)).expandY().fillY();
        table3.add(new Label("", skin)).width(10f).expandY().fillY();// a spacer
        table3.add(new Label("Valyrian steel..", skin)).expandY().fillY();


        //inner table that is used as a makeshift list.
        Table innerContainer = new Table();
        innerContainer.add(table1).expand().fill();
        innerContainer.row();
        innerContainer.add(table2).expand().fill();
        innerContainer.row();
        innerContainer.add(table3).expand().fill();

        // create the scrollpane
        scrollpane = new ScrollPane(innerContainer);

        //add the scroll pane to the container
        container.add(scrollpane).fill().expand();

        // setup stage
        stage = new Stage();

        // add container to the stage
        stage.addActor(container);

        // setup input processor (gets clicks and stuff)
        Gdx.input.setInputProcessor(stage);

        // setup a listener for the tables with out data

        table1.addListener(new FocusListener(){
            @Override
            public boolean handle(Event event){

            if (event.toString().equals("mouseMoved")){
                table1.background(new TextureRegionDrawable(new TextureRegion(new Texture("gray.png"))));
                return false;
            }
            else if(event.toString().equals("exit")){
                //table1.setBackground(null);
                //table1.background("");
                table1.setBackground(null, false);

                return false;
            }
                return true;
            }

        });
        table2.addListener(new FocusListener(){
            @Override
            public boolean handle(Event event){

            if (event.toString().equals("mouseMoved")){
                table2.background(new TextureRegionDrawable(new TextureRegion(new Texture("gray.png"))));
                return false;
            }
            else if(event.toString().equals("exit")){
                //table1.setBackground(null);
                //table1.background("");
                table2.setBackground(null, false);

                return false;
            }
                return true;
            }

        });
        table3.addListener(new FocusListener(){
            @Override
            public boolean handle(Event event){

            if (event.toString().equals("mouseMoved")){
                table3.background(new TextureRegionDrawable(new TextureRegion(new Texture("gray.png"))));
                return false;
            }
            else if(event.toString().equals("exit")){
                //table1.setBackground(null);
                //table1.background("");
                table3.setBackground(null, false);

                return false;
            }
                return true;
            }

        });
    }

    @Override
    public void hide() {
    }

    @Override
    public void pause() {
    }

    @Override
    public void resume() {
    }

    @Override
    public void dispose() {
    }

}