1. I know you are just giving examples, but do be careful with the IF field
syntax:
a. Despite what some examples may show, you are generally better off using

{ IF { MERGEFIELD field1 }
or
{ IF { REF field1 }
than
{ IF field1
or if you are testing string values, use
{ IF "{ MERGEFIELD field1 }"
or
{ IF "{ REF field1 }"

b. always have a space either side of the comparison operator:
{ IF "{ MERGEFIELD field1 }" = "BLAH"

2. In answer to the question you actually asked, suppose you want

{If FIELD1="BLAH" OR
FIELD2="BLAH" "BLAH" ""}

you can either use the obvious nested IF:

{ IF "{ MERGEFIELD FIELD1 }" = "BLAH"
"BLAH"
"{ IF "{ MERGEFIELD FIELD2 }" = "BLAH"
"BLAH"
"" }" }

For
{If FIELD1="BLAH" AND
FIELD2="BLAH" "BLAH" ""}
you could use

{ IF "{ MERGEFIELD FIELD1 }" = "BLAH"
"{ IF "{ MERGEFIELD FIELD2 }" = "BLAH"
"BLAH" "" }"
"" }
or you can think in terms of generating 0/1 values using COMPARE fields,
then using {=} fields with "and" and "or" functions to test the results,
nested within an { IF } field.

There are limits to the level of nesting (20 I think)

Alternatively, you may be able to use Access queries that use iif functions
etc. to do the same thing and use the queries as the data source for your
merge.

--
Peter Jamieson - Word MVP