二百十日 is read as にひゃくとおか. What about 百十日 or 三百十日?

As your links say, both 二百十日 and 二百二十日 are the names of certain folk calendrical terms (210th and 220th days from 立春).

Here, the date counter ～か is used to indicate a day in the calendar. Since there is no serial date bigger than 31 in either Gregorian or Japanese months, thinking about such big dates is usually meaningless. However, those specific two words you mentioned are the only examples* that rightly represent that definition: 210/220th calendrical day (of a year). You can either say that those two are exceptional fixed expressions, or that you may use it when we adopt an ordinal date system in our daily life, but it is only hypothetical.

Besides that, you cannot use ～か form as a part of bigger numbers when calculating days in general:

百[八日]{はちにち}間修行した had training for 108 days
無人島に漂流して百[二十日]{にじゅうにち}め the 120th day since cast away on a no man's island

But 四日{よっか} is usable in any case, for some reason:

無人島に漂流して百二十[四日]{よっか/よんにち}め

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* ^{Unless you count in 十月十日}.

1. As you expected, these can be read as とおか but it is not commonly used in daily life.

2. Same as 1. => We say とおか or はつか etc. only 十日 or 二十日, respectively.

3. 六十日=むそか (commonly ろくじゅうにち)，七十日=? (even Japanese don't know. ななじゅうにち or しちじゅうにち are used)，九十日=?

Special case (commonly used now):

• 初七日=しょなのか (the first seventh day when the soul of a dead person comes to Sanzu no River)
• 四十九日=しじゅうくにち (the day when the soul of a dead person arrive at paradise(極楽浄土).)

In a Buddhist mass, such ways of calling are used.