Okay, so I have figured this out myself. (A tad disappointed that I didn't get any answers, but I'm well over it now...) So, again, I'm publishing the outcome of my research here, in case anyone else is interested.

Umbraco.MultipleMediaPicker images - IContent.SetValue

The clue here is to first save your image files as IMedia, then put together a comma separated string with the ids of those IMedia. This string is your input to SetValue for your property:

    // "Shortcuts" for the services we need
    IContentService cs = ApplicationContext.Current.Services.ContentService;
    IMediaService ms = ApplicationContext.Current.Services.MediaService;

    // Your content node
    IContent yourContentNode = ...

    // CSV string that lists the image media IDs
    string imageIds = "";

    // Loop through image files
    foreach (string imagePathname in imagePathnames)
    {
        string imageFilename = Path.GetFileName(imagePathname);
        if (System.IO.File.Exists(imagePathname))
        {
            // Read the image file through a file stream
            using (FileStream imageStream = new FileStream(imagePathname, FileMode.Open, FileAccess.Read))
            {
                // Stream the file into a new umbraco media item
                IMedia imageMedia = ms.CreateMedia(bildeFilename, medHavnFolder.Id, "Image");
                imageMedia.SetValue("umbracoFile", imageFilename, imageStream);
                ms.Save(imageMedia);
                imageStream.Close();
                if (!string.IsNullOrWhiteSpace(imageIds))
                    imageIds += ", ";
                // Add id of this media item to the list
                imageIds += imageMedia.Id;
            }
        }
    }

// Set the property value to this list of media ids
if (!string.IsNullOrWhiteSpace(imageIds))
    yourContentNode.SetValue("YourMultipleMediaPickerPropertyName", imageIds);
// Dont ever forget to publish your content node!
    cs.Publish(yourContentNode);

Hope it's understandable.

Umbraco.CheckBoxList - IContent.SetValue

The clue here is to put together a CSV string with the IDs - not the values - of the items you want to be checked. To do this you have to get a list of all the prevalues and their ids, then do a lookup from value to id to make the list of ids.

// Get the pre-values for your checkbox list in a Dictionary for lookup
// <your property id> can be found by hovering over the property name in design mode in backoffice for your document type
var yourPropertyPrevaluesRootIterator = umbraco.library.GetPreValues(<your property id>);
yourPropertyPrevaluesRootIterator.MoveNext();
var yourPropertyPrevaluesIterator = yourPropertyPrevaluesRootIterator.Current.SelectChildren("preValue", "");
Dictionary<string, string> yourPropertyPrevalues = new Dictionary<string, string>();

while (yourPropertyPrevaluesIterator.MoveNext())
{
    yourPropertyPrevalues.Add(yourPropertyPrevaluesIterator.Current.Value, yourPropertyPrevaluesIterator.Current.GetAttribute("id", ""));
}

// Now you can add items to check like this:
string checkItemsIds = "";
checkItemIds += yourPropertyPrevalues["Some value to be checked"];
checkItemIds += ", " + yourPropertyPrevalues["Some other value to be checked"];    

// And finally set your property
yourContentNode.SetValue("<your property name>", checkItemIds);

// Dont ever forget to publish your content node!
cs.Publish(yourContentNode);

I wrote this code directly in the forum editor, based on my own code which is slightly more complicated. So, if it doesn't compile or doesn't make sense, please don't hesitate to ask!

Just a quick addendum/improvement. I wasn't quite satisfied with the hardcoded datatype id, so I figured out a better way: find the id by the datatype alias.

IDataTypeService dts = ApplicationContext.Current.Services.DataTypeService;

IEnumerable<IDataTypeDefinition> allDataTypes = dts.GetAllDataTypeDefinitions();
int yourPropertyDataTypeId = allDataTypes.Where(dtd => string.Compare(dtd.Name, "Your property datatype alias", true) == 0).First().Id;

Then you can say umbraco.library.GetPreValues(yourPropertyDataTypeId)

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