I did some research using the Corpus of Historical American English to see if I could track the history of these words. Each of these words has a different story to tell.
DREAMED and DREAMT
See the raw data (Google Docs)
In the early 1800s, dreamt was more common than dreamed but by the mid-1800s, dreamed was much more common and has stayed so since. While there is nothing wrong with continuing to use dreamt, dreamed is definitely the more common form.
LEAPED and LEAPT
See the raw data (Google Docs)
Leaped has long been more popular than leapt, though leaped has been in decline since 1900, and leapt has been on the increase since 1950, and today they are about equally common. It is likely that if the current trends continue, leapt will become decisively more common than leaped within a decade or two. Indeed, in the Corpus of Contemporary American English, leapt has 484 incidences for 2005-2010 and only 460 for leaped. So, both are about equally common these days and you are in good company if you prefer leapt.
SWEEPED and SWEPT
Neither COCA nor COHA have any results for sweeped, nor does any dictionary I checked list sweeped as a possible past tense form for sweep. Sweeped doesn’t appear to have had any currency in American English since 1810. Google reports only 43,000 results for sweeped compared with 78,000,000 for swept.
LIGHTED and LIT
See the raw data (Google Docs)
Apparently, lighted was much more popular than lit, from the early 1800s until about 1940. During this time lit was steadily gaining popularity, while lighted began a precipitous decline in 1940. Today, lit is much more popular than lighted, so if you prefer lit, you are in very good company. However, there would be trouble objecting to lighted on historical grounds, as lighted was by far the most common form until the 1940s.
These examples are a minefield, because lay and lie have the most confusing similar meanings and even overlapping past tense forms. Many people do not use them in the standard ("correct") way, and don't even know the right way. You don't always use the same verb between lay and lie in your examples, and you don't always use the right one in the right place, so I will try to explain those as well.
Technically speaking, the correct way to form the first sentence is:
When she walked in, he was lying on the bed.
The grammarian standard rule is that lie is used when the actor or subject of the sentence is the one who is lying down (which is what is happening in your sentence).
Now, with this correction in mind, on to the answer: technically all of your sentences are correct, but they all mean a different thing.
You use the past progressive when you want to describe an event in the past that took place during another event in the past. So, in your first sentence, "she walked in" is one event that happened, and "he was lying on the bed" means that the walking-in happened during the lying.
In your second sentence, you are have two simple past tense verbs. This time, "was laid" is a passive construction in the past tense (past tense of "lay", specifically). Since the sentence is passive, it means that someone laid "him" on the bed — he didn't do it himself — so the past tense of lay (rather than the past tense of lie) is the correct verb to use. So, this sentence means that at the moment she walked in, someone or something laid him on the bed.
In your third sentence, you again have two past tense verbs. The verb lay is the simple past form of lie, so you are saying that the walking-in and the lying happened at the same moment in the past.
Best Answer
Shew was once the most common past participle of show, with shewn also appearing and shew or shewed for the past tense.
It also has a long use as the present tense.
For added confusion, shew seems to have changed pronunciation before it changed spelling, so if you come across shew in an older text you can't be sure whether it would be pronounced /ʃuː/ or pronounced /ʃəʊ/.
It remained very common for a long time especially in Scotland, north England, and Ulster but also various other places throughout the English-speaking world, particularly rural.
The Ulster part has an interesting example, there were propaganda posters around the time of the Treaty by those who wanted to remain in the United Kingdom and who were mostly in North East Ulster—the partition that created Northern Ireland having come about as a compromise between their concerns and that of the rest of the island—which would use "we'll shew 'em" precisely because it was a form more likely to be found among Ulstermen than among other Irishmen. (Though it would still have been common enough south of the future border then, as well).
It's increasingly rare as more standardised education increasingly deems it "wrong", but it's certainly not surprising to find.
Glew I have only heard of being used as a present-tense verb (now obsolete) or as the past of glow meaning "to stare" (now mostly obsolete). I wouldn't be amazed to hear that some dialect that had shew instead of showed or shown had a from glew instead of glowed modelled after it.