It's not at all uncommon not to find four-word phrases in dictionaries, unless they are idioms. When I was younger, dictionaries would define words, and only occasionally deal with definitions beyond single words.
Yes, they are standard English.
If you'd like to give the sentences you found them in, we can explain the phrases.
1a. from the inside out
2a. from the top down
3a. from the bottom up
respectively different from:
1b. out from the inside
2b. down from the top
3b. up from the bottom
? Suppose context is a house on fire. Then for these pairs:
4a. The fire spread from the insideout.
4b. The fire spread outfrom the inside .
5a. The fire spread from the topdown.
5b. The fire spread downfrom the top.
6a. The fire spread from the bottomup.
6b. The fire spread upfrom the bottom .
1. The other phrases aren't different, but we don't normally say them like that.
In your completely literal examples of the fire, you could use either.
Here are some other uses which normally use the word order you gave originally:
a. Some people think that a microwave oven cooks from the inside out, but it actually cooks like a conventional oven, from the outside in.
b. Some software is developed from the top down - the broad outline is coded first, then the next level down, etc. Other software is developed from the bottom up - the final procedures are coded first, then they are added together into a higher layer, etc.
c. Learning a language by learning vocabulary and grammar is learning it from the bottom up. Learning it by exposure to sentence patterns in speech and writing is learning it from the top down. [I'd advise a combination of both.]
So, these terms can be used in abstract ways, depending on what one considers "the top" or "the inside" etc.