I would export every file locally first. Then I would first try to import them to Episerver with the same relative URL if possible. Since you can set the URL segment on a new content item in Episerver it might be possible. If it works you don't need to worry about breaking any links to images which is really nice.

If not possible for some reason I would import them to Episerver in some other structure but store an external identifier on the content in Episerver that contains the id of it in Sitecore as well as the old relative Url in a separate property. Then I would rewrite any links in texts etc. Probably best to do that in the json format before importing.

I'd solve this in different ways depending on the pure volumn of image content.  Since you've already written an import routine to process the content, you could extend it to also download and save the images directly into the CMS. 

There is a nice easy start article that you could look at here: https://marisks.net/2017/07/13/programmatically-upload-image-to-episerver/ but you'd need to extend it into also creating and navigating the media asset folders to maintain the same image folder structure.  When you call contentRepository.GetDefault<T>(SiteDefinition.Current.GlobalAssetsRoot), you can replace SiteDefinition.Current.GlobalAssetsRoot with the content reference for the folder you want the image to be accessible in.

Thanks Stotty and Daniel. Is there a way we can upload video programatically?

Theoretically It should be no different to uploading an image, but there is a ~2GB limit on the MemoryStream object due to the use of int32 for indexing.  So you'll need to consider the size of your largest media asset.  If the video's are too large, then you may need to manually upload them, at which point you'll need to override the maximum request length in your web.config for the EPiServer path:

<location path="EPiServer">
	<system.web>
		<httpRuntime maxRequestLength="1000000" requestValidationMode="2.0" />
	</system.web>
	<security>
		<requestFiltering>
			<!-- IIS settings, specifies the maximum length of content in a request in bytes, default value is 30000000 -->
			<requestLimits maxAllowedContentLength="1024000000" />
		</requestFiltering>
	</security>
</location>