Unless these files are very large and performance is critical, reading them by line can be accomplished easily via the ADODB.Stream object.
Not only will this handle several line delimiters (Stream.LineSeparator = adCR, adCRLF, or adLF) it can also be used to process files containing Unicode (UTF-16), UTF-8, system codepage ANSI, and alternative "ANSI" encodings for other locales.
For example if you have a text file that contains "ANSI" from a Russian language locale you can set Stream.Charset = "koi8-r" and read the data with proper translation into VB6 Unicode (UTF-16):
Dim Stm As ADODB.Stream
Dim Line As String
Dim Counter As Long
Set Stm = New ADODB.Stream
With Stm
.Open
.LoadFromFile "russian.txt"
.Type = adTypeText
.Charset = "koi8-r"
.LineSeparator = adLF
Do Until .EOS
Line = .ReadText(adReadLine) 'Text is in Unicode now.
Counter = Counter + 1
Loop
.Close
End With
Charset defaults to the value "unicode" (UTF-16) but to read or write the Stream in ANSI with the default codepage you can set it to "ascii" instead.
HKCR\MIME\Database\Charset contains the available values.