Search Engines

Yes, you can still access the definitions freely online, since apparently Google and Bing are still licensed to provide them. (Note: Some entries for proper nouns are missing or incomplete in Google, while Bing's were complete.)

For best results, search for define [term]. You can also search for dictionary and type your word in the box (autocomplete will show you what words are in the dictionary).

Here's what I see in Google compared with NOAD (they're the same, though I wasn't able to show the full NOAD entry which includes the origin):

From define whipping boy

ODE vs NOAD

It's not entirely clear to me how this works, but I think it's identical to NOAD for most definitions. (For people who live elsewhere, it may use something based on ODE instead, the British counterpart to NOAD.) Unfortunately, Lexico had some definitions that were missing in NOAD/ODE, such as "fireman's pole".

For your convenience I made bookmarklets to switch between dictionaries, based off the information in Nardog's answer. To use, bookmark any page and replace the URL with one of the snippets below.

Switch to British English:

javascript:window.location=window.location.toString().includes('gl=us')?window.location.toString().replace(/gl=us/,'gl=gb'):window.location.toString()+'&gl=gb'

Switch to American English:

javascript:window.location=window.location.toString().includes('gl=gb')?window.location.toString().replace(/gl=gb/,'gl=us'):window.location.toString()+'&gl=us'

(Could probably use fine tuning.)

Attribution

If you use a definition in your post, please credit the dictionary provider, which you can see at the top: "Definitions from Oxford Languages". For greatest clarity I recommend citing how you found the definition: "Oxford Languages via Google".

Finding example sentences

Lexico had more example sentences, and sadly I don't think they are available anywhere else. No other dictionary has examples quite like that. The closest alternative may be Cambridge, which seems to have about two examples per definition, plus a few more that belong to each group of definitions. However, while Lexico had "found" examples, Cambridge seems to have examples that were made up for the dictionary.

Operating systems that include Oxford Dictionaries

Some systems also come with Oxford Dictionaries installed. This is usually a more convenient way of accessing it. Here's a list:

• MacOS
• iOS (as I'm using in the screenshot)
• Kindle

Apps

As you noted, there are also mobile apps (iOS and Android). I may have used the Android one but I honestly don't remember much about it. The reviews seem to be very mixed.

Archive sites

Lastly, many of the pages (but not all) were backed up by archivers like archive.org. For the best chance to find an archive, it's important to remember all the renames the site went through:

• lexico.com
• oxforddictionaries.com (can't get it to list all the definitions)
• en.oxforddictionaries.com