I assume that by "fastest" you mean run-time:
The fastest way to do this from compiled code is to use the SQLBulkCopy methods to insert the data directly into your target table. You will have to write your own code to open and read the source file and then split it into the appropriate columns according to their fixed-width offsets and then feed that to SQLBulkCopy. (I think that I have an example of this somewhere, if you want to go this route)
The fastest way to do this from T-SQL would be to shell out to DOS and then use BCP to load the file directly into your target table. You will need to make a BCP Format File that defines the fixed-width columns for this appraoch.
The fastest way to do this from T-SQL, without using any CLI, is to use BULK INSERT to load the file into a staging table with only one column as DATA VARCHAR(MAX)
(make that NVARCHAR(MAX) if the file has unicode data in it). Then execute a SQL query you write to split the DATA column into its fixed-width fields and then insert them into your target file. This should only take a single INSERT statement, though it could be a big one. (I have an example of this somewhere as well)
Your other 'fastest' option would be to use an SSIS package or the SQL Server Import Wizard (they're actually the same thing, under the hood). SSIS has a pretty steep learning curve, so it's only really worth it if you expect to be doing this (or things like this) for other cases in the future as well.
On the other hand, the Wizard is fairly easy to use as a one-off. The Wizard can also make a schedulable job, so if you need to repeat the same thing every night, that's certainly the easiest, as long as it actually works on your case/file/data. If it doesn't then it can be a real headache to get it right, but fixed-width data should not be a problem.
The fastest of all of these options has always been (and likely will always be) BCP.
BULK INSERT [#MyTestTable] FROM 'D:\MyTextFile.txt'
. Provided you can massage the data into a parsable format for bulk, it should be fine. – Purpurin