1st 1877: Orchard, 11; Wurm, 8; drawn, 3
Concluded before 15 April 1877 (probably March 1877).
http://www.edochess.ca/matches/m277...

2nd 1877: Wurm, 9; Orchard, 3; drawn, 1
Concluded before 15 April 1877 (probably March/April 1877).
http://www.edochess.ca/matches/m461...

3rd 1877: Orchard, 7; Wurm, 5; drawn, 1*
Orchard - Wurm (1877)
Games exist for 4/15, 4/18, 4/19 and two additional April games (probably started in April 1877).
http://www.edochess.ca/matches/m461...

No evidence exists for a 11-10 match played in late 1877.
Best guess is the Illustrated London News misreported Wurm's score from the 1st match.
One of the games given by the ILN for this supposed 11-10 match is identified by Orchard as coming from the 1st match.

4th 1883: Wurm, 7; Orchard, 1; drawn 3
11 June 1883—18 June 1883.
Wurm - Orchard (1883)
http://www.edochess.ca/matches/m461...

5th 1887: Wurm, 5; Orchard, 1; drawn, 2
29 August 1887—9 September 1887.
Wurm - Orchard (1887)
http://www.edochess.ca/matches/m277...

6th 1888: Wurm, 5; Orchard, 3; drawn, 2
16 November 1888—28 November 1888.
Game Collection: Wurm - Orchard (1888)
Wurm - Orchard (1888)
http://www.edochess.ca/matches/m311...

7th 1891: Orchard, 7; Wurm, 4; drawn 2
2 February 1891—16 February 1891
Orchard - Wurm (1891)
http://www.edochess.ca/matches/m311...

* The number of draws are still undetermined for this third match, but at least one draw must exist as the game given in the Sunny South as being played on 15 April 1877 was a draw and it must have been from this third match and not from the prior two matches (or an off-hand game if the date is correct).

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In regards to the earliest three matches, the first two results were documented in Brownson's Chess Journal and must have been completed prior to the report given in the Macon Telegraph of 15 April 1877 (see below). The third match was for seven games up, with the 12th non-drawn game played on 19 April 1877 concluding the match (per Wurm's column). I'm not sure what to make of the report from the Illustrated London News, 1877.10.13, giving the 11 to 10 score; perhaps some off-hand non-match games were added to one of the match totals (more research is underway).

As for the remaining four matches, the report given in the Newark Sunday Call, 22 February 1891, giving an accumulated score over 'the four matches now played' of +21-12=10 for Wurm, the draw counts are accurate for the 1883, 1887 and 1891 matches, however, I only have two reports regarding the totals for the 1888 match (see Cincinnati Commercial Gazette, 1888.12.08; Charleston Sunday News, 1888.12.09), whereas I have daily accounts of the game results for the other three matches (see 1883, 1887 and 1891 matches). I suspect the Newark Sunday Call just made an arithmetic error and there is no missing draw to be placed in these four matches.


First three match materials:
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It may interest our chess friends to read a chess item from Atlanta. A Northern player, Mr. I. E. Orchard, on a visit there, has been contesting a couple of matches with Mr. Wurm, of Atlanta. The first match resulted in the defeat of Atlanta by a score of eleven to eight, but the return match proved a victory for the Atlanta player by the handsome majority of nine to three. We congratulate Atlanta, as we understand Mr. Orchard to be a fine player. He was a contestant in the late international tourney at Philadelphia.
Source: <Macon Telegraph and Messenger>, 1877.04.15, p7
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The Sunny South is a weekly newspaper published in Atlanta, George. ... From it's issue of April 21st we learn that two friendly matches have taken place during the past month at the rooms of the Young Men's Library, in Atlanta, between Mr. I. E. Orchard, of Columbia, South Carolina, and Mr. A. F. Wurm, of Atlanta, Ga. These contests resulted as follows:

First Match—Orchard 11; Wurm, 8; drawn, 3.
Second Match—Orchard, 3; Wurm, 9; drawn, 1.

Mr. Orchard won a majority of the off-hand games.
Source: <Brownson's Chess Journal>, n77, May 1877, p188
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The following pair of interesting Games occurred in a match played recently between Messrs. Orchard and Wurm, two of the strongest players in the Southern States of America. The match was won by Mr. Wurm, with a score of eleven games to ten.
Source: <Illustrated London News>, 1877.10.13, p367
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Between I. Edward Orchard, of Columbia, S. C., and A. F. Wurm, Atlanta, Ga., played in Atlanta, April 19, 1877. ...

The loss of this game was most trying to Mr. Wurm from the fact that the score stood: Orchard 6, Wurm 5, and the match to consist of 7 won games.
Source: (Atlanta) <Sunny South>, 1878.04.20
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All CG games played between Orchard and Wurm:
https://www.chessgames.com/perl/che...

Orchard at edochess:
http://www.edochess.ca/players/p153...

Wurm at edochess:
http://www.edochess.ca/players/p312...